PELPS Ill. A Microcomputer Price Endogenous Linear Programming System for Economic Modeling Version 1.0. Dali Zhang Joseph Buongiorno Peter J.

Transcription

1 United States Department of Agriculture Forest Service Forest Products Laboratory Research Paper FPL-RP-526 PELPS Ill A Microcomputer Price Endogenous Linear Programming System for Economic Modeling Version 1.0 Dali Zhang Joseph Buongiorno Peter J. lnce

2 Abstract This document provides documentation and user information for PELPS III, a microcomputer Price Endogenous Linear Programming System for economic modeling. Originally developed for the North American pulp and paper industry, PELPS III can be used for any sector to predict consumption, production, and capacity by technology, and trade within or among several regions or countries. The theoretical structure is that of spatial equilibrium modeling under competitive market assumptions. This document contains a detailed user s guide, an application of PELPS III, and a mathematical description of the model. A glossary of terms is also included. Acknowledgments We thank K. Gilless and P. Calmels for their contributions to the earlier versions of PELPS, and W. Lange, K. Skog, D. Roberts, R. Jacques, and S. Phelps for their support and collaboration. Key Words: Economic model, linear programming, spatial equilibrium, international trade, prices, demand, supply, capacity, technology, recycling, industry, pulp and paper October 1993 Zhang, Dali; Buongiorno, Joseph; Ince, Peter J PELPS III: A microcomputer price endogenous linear programming system for economic modeling. Res. Paper FPL-526. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 43 p. A limited number of free copies of this publication are available to the public from the Forest Products Laboratory, One Gifford Pinchot Drive, Madison, WI Laboratory publications are sent to more than 1,000 libraries in the United States and elsewhere The Forest Products Laboratory is maintained in cooperation with the University of Wisconsin. The policy of the United States Department of Agriculture Forest Service prohibits discrimination on the basis of race, color, national origin, age, religion, sex, or disability, familial status, or political affiliation. Persons believing they have been discriminated against in any Forest Service related activity should write to Chief, Forest Service, USDA, P.O. Box 96090, Washngton, DC

3 Contents Introduction... What is PELPS III?... Static Phase... Dynamic Phase... User's Guide Manufacturing Cost Transportation Cost Material Balancing Constraints and Prices.. 32 Manufacturing Capacity Constraints Recycling Constraints Stepwise Approximation of Demand and Supply Getting Started... 3 Dynamic Phase Hardware and Software Requirements... 3 Installing PELPS III... 3 Starting PELPS III... 4 Quitting PELPS III... 4 Defining Run-Time Parameters... 4 Entering Data... 5 Shifts in Demand Shifts in Supply Changes in Exchange Rate Changes in Manufacturing Cost Changes in Transportation Cost Changes in Manufacturing Capacity Changes in Recovery Rate Changes in Other Parameters Demand... 5 Supply... 6 Manufacture Capacity Capacity Recycling (Demand) Recycling (Supply) Transportation Cost and Tax Exchange Rate Exogenous Changes Glossary... References Saving Data... Solving Base-Period Equilibrium... Solving Multiperiod Equilibria... Retrieving Data Application to North American Newsprint Industry Regions Commodities Processes Data Results Mathematical Models... Static Phase... Objective Function... Demand... Supply

4 PELPS III A Microcomputer Price Endogenous Linear Programming System for Economic Modeling Version 1.0 Dali Zhang, Research Associate Joseph Buongiorno, Professor University of Wisconsin-Madison Peter J. Ince, Research Forester Forest Products Laboratory Introduction What is PELPS III? The price endogenous linear programming system, PELPS III, is a general microcomputer system for modeling economic sectors. It is the successor of PELPS (Gilless and Buongiorno 1985), PELPS II (Calmels and others 1989), and PELPS II PLUS (Zhang and others 1990). PELPS III is based on price endogenous linear programming--a method for combining regional information on supply and demand curves, manufacturing technologies, and transportation costs into spatial sector models. Variants of this method have been used to model a number of agricultural and energy-related sectors (Kennedy 1974; McCarl and Spreen 1980). PELPS III also extends concepts that have been applied in previous interregional models of the forestry sector, such as the Timber Assessment Market Model (Adams and Haynes 1980) and the Global Trade Model (Kallio and others 1987). Although PELPS III was first developed to model the North American pulp and paper sector, it is a very general system, and with appropriate data it can be applied to any other sector of the economy. Therefore, the system is of potential value to many academic and industrial economists and researchers. PELPS III has a static and a dynamic phase. In the static phase, it computes a multiregion, multicommodity equilibrium: the quantities and prices that clear all markets at a given point in time. In the dynamic phase, it predicts the evolution of this spatial equilibrium over time. For example, for comparative static problems, two computations under different sets of assumptions are sufficient to show the long-term effect of an import tax (other things being equal). The dynamic phase is needed to predict how a sector adjusts gradually to changes in exogenous variables. This is especially important to predict changes in capacity, since actual capacity always lags behind desired capacity, due to the time needed to install new capacity.

5 Static Phase The static phase of PELPS III solves a generalized version of Samuelson's (1952) classical spatial equilibrium problem, for which... we are given at each of two or more localities a domestic demand and supply curve for a given product (e.g., wheat) in terms of its market price at that locality. We are also given constant transport costs (shipping, insurance, duties, etc.) for carrying one unit of the product between any two of the specified localities. and from which we wish to know What then will be the final competitive equilibrium of prices in all the markets, of amounts supplied and demanded at each place, and of exports and imports? PELPS III generalizes this problem to represent the production, transport, transformation, and consumption of several commodities. A commodity may be either a primary raw material (such as pulpwood), a recovered waste (such as waste paper), or a consumed commodity (such as newsprint). Consumed commodities may be described as virgin commodities (made only of new raw material, such as virgin pulp) or recycled commodities (made of recovered wastes, such as recycled paper) or commodities that combine virgin and recycled inputs. In PELPS III there are several demand regions and supply regions in which the demand (supply) of a commodity is described by an equation that gives quantity demanded (supplied) as a function of price. The supply of recovered wastes is constrained by the amount of materials available and by recovery policies. The demand of recycled commodities is constrained by recycling policies. PELPS III also has manufacturing regions, where the production of a commodity, and the consumption of the commodities needed to make it, is modeled as a process described by activity analysis (as in Takayama and Judge 1964). Each process has a limited capacity. Within a process, a commodity can be made with different combinations of inputs, or input mixes, defined by manufacturing coefficients giving the amount of each input needed per unit of output. To each input mix corresponds a unit manufacturing cost. PELPS III explicitly models the shipment of commodities between regions. The unit transportation cost includes freight and import or export taxes. Exchange rates are recognized explicitly, so international models are possible. The solution of the static phase of PELPS III is obtained by price endogenous linear programming (Hazell and Norton 1986). By maximizing the sum of producer and consumer surplus throughout the sector, it gives the equilibrium quantities produced, transformed, transported, and consumed. The static phase also gives the corresponding prices that clear all markets at a given point in time, subject to the positions of supply and demand curves, the capacities of production by region and process, the manufacturing and transportation costs, the taxes and exchange rates, and the recycling constraints. Dynamic Phase In its dynamic phase, PELPS III breaks down a multiperiod spatial equilibrium problem into a sequence of problems, as in the "recursive programming" approach of Day (1973). This recursive formulation, which simulates partial long-run optimization 2

6 behavior, also allows a user to include sufficient detail in a model and thus enhance the possibility of successful implementation. Thus, the dynamic phase of PELPS III is a succession of static phases, one for each period in the forecast. The static calculation in a period gives the short-term equilibrium, subject to the demand, supply, costs, and capacity in that period. The parameters of the programming problem that condition the equilibrium change from period to period, due to exogenous changes (shifts in demand related to population and income growth, shifts in supply, and changes in costs, taxes, and exchange rates) and to capacity changes determined endogenously by the model. The capacity of production in the next period is a function of the shadow price of capacity in the previous period, past production, and the cost of capacity increase. Thus, PELPS III simulates the rational behavior of suboptimizing agents who forecast the future imperfectly, based on past information. User's Guide Getting Started PELPS III is designed as a menu-driven system, and therefore it facilitates modeling. PELPS III is available in two versions: PELPS III for DOS and PELPS III for Windows. The latter takes advantage of the capabilities of Microsoft Windows TM and Lotus for Windows TM. Hardware and Software Requirements To use PELPS III for DOS, you need A DOS system computer with a math coprocessor, a hard disk drive, and a floppy disk drive At least 640 KB of RAM (conventional memory) Lotus Release 3.0 or later HYPER LINDO/PC (LINDO is a trademark of Lindo Systems Inc. (Schrage, 1986)) To use PELPS III for Windows, you need A DOS system computer with a math coprocessor, a hard disk drive, and a floppy disk drive 2 MB of RAM (640KB of conventional memory), 4MB recommended Microsoft Windows version 3.0 or later Lotus for Windows Release 1.0 or later HYPER LINDO/PC In addition, a mouse is recommended, but not required. Installing PELPS Ill Use the PELPS III Install program to install the PELPS III files on your computer. Before installing PELPS III, make sure that 3

7 the LINDO and Lotus directories are in the DOS path, the COMMAND.COM file is in the root directory of the C drive, the two statements buffers=32 (or greater) and files=20 (or greater) are in the CONFIG.SYS file, and there is no PELPS directory on the C drive prior to the installation of PELPS III. Then, reboot your computer and insert the PELPS III diskette in either Drive A or Drive B. Type a:installa or b:installb, depending which disk drive you use. Press [ENTER]. If you use PELPS III for Windows, to exit Windows automatically after you save the input file and quit Lotus for Windows, you must have SYSTEML.INI file in the subdirectory of Windows, C:\WINDOWS. The file SYSTEML.INI is the same as SYSTEM.INI, except for the following statement: Shell=PROGMAN.EXE in SYSTEM.INI Shell=123W.EXE in SYSTEML.INI To create the SYSTEML.INI file, you can first copy C:\WINDOWS\SYSTEM.INI to C:\WINDOWS\SYSTEML.INI and then modify the above shell statement using a text editor. Starting PELPS III You must start PELPS III from the DOS prompt in the C:\PELPS subdirectory. Within this subdirectory, type pelpswin (or PELPSWIN) to run PELPS III for Windows or pelpsdos (or PELPSDOS) to run PELPS III for DOS, and then press [ENTER]. The PELPS III main menu will appear on the screen. It contains seven options: 1. Edit or create input file 2. Define run-time parameters 3. Run base-period 4. Run multiperiods -- accelerator model 5. Run multiperiods -- q model 6. Edit output file 7. Quit PELPS III Quitting PELPS III To quit PELPS III, choose option 7 (Quit PELPS III) from the main menu. Defining Run- Time Parameters Before solving a problem using PELPS III, you need to define the following parameters by choosing option 2 (Define run-time parameters) from the PELPS III main menu: 1. Solution range: the range of quantities within which supply and demand equations are approximated by linear steps. For example, a value of 0.5 means that the stepwise approximation is done between 0.5 and 1.5 times the previous equilibrium quantity. Outside that range, demand and supply equations are horizontal (within 4

8 the user-specified bounds). 2. Number of steps: the number of steps used in the stepwise approximation of the demand and supply curves. The largest number of steps is 26. A large number of steps for a given solution range increases the precision of the results but also increases the size of the problem and decreases the speed of the program. In general, 15 to 20 steps are appropriate for most problems. 3. Length of projection: the number of periods in a multiperiod forecast. The maximum length is 55 periods. Periods can be of any length of time, e.g., 6 months, 1 year, or 5 years, as long as all data are consistent with the time unit. Entering Data PELPS III uses Lotus for data entry and retrieval, which facilitates data editing. Option 1 (Edit or create input tile) in the main menu brings the Lotus worksheet file Auto 123 onto the screen. With this file you can create or modify an input data file for PELPS III. You may also use a text editor to organize your input data. However, you must follow the required format. The input data file consists of 10 worksheets: 1. DEMAND (required) 2. SUPPLY (required) 3. MANUFACTURE (optional) 4. CAPACITY 1 (optional) 5. CAPACITY 2 (optional) 6. RECYCLING (DEMAND) (optional) 7. RECYCLING (SUPPLY) (optional) 8. TRANSPORTATION COST AND TAX (optional) 9. EXCHANGE RATE (required) 10. EXOGENOUS CHANGE (optional) Each worksheet is organized as follows: Demand Worksheet A (Table 1) contains the data that define each demand equation. The table includes the following: a base demand quantity; the corresponding base demand price expressed in a common currency (e.g., US$); elasticities with respect to price, up to three other shift variables of your choice, and last-period demand; and a lower bound. Of the elasticities, only the price elasticity is needed to calculate a static equilibrium. The other elasticities are needed in dynamic, multiperiod forecasts. PELPS III allows you to define several types of short-term demand curves (Fig. 1). Curve (a) represents a typical demand function, while curves (b) to (e) are special cases. You define curve (a) with one point (Q 0, P o ) and a price elasticity. Curve (b) is the same as (a) with a lower bound on the quantity demanded, Q L. Curve (c) is curve (b) with the price elasticity being equal to infinity. You define such a demand curve by entering a base-period (reservation) price (P o ), 0.00, as the price elasticity, and a lower bound (Q L). 5

9 Table 1. Data for demand equations. A A B C D E F G H I J K ****** DEMAND ****** A : Region number (01 to 99, in acending order) B : Commodity number (01 to 99, in ascending order within each region) C : Base period price in common currency D : Base period quantity demanded at price C E : Price elasticity (<0, enter 0.00 for horizontal demand) F : Elasticity of demand with respect to the first shift variable (optional, enter 0.00 if omitted) G : Elasticity of demand with respect to the second shift variable (optional. enter 0.00 if omitted) H : Elasticity of demand with respect to the third shift variable (optional, enter 0.00 if omitted) I : Elasticity of demand with respect to previous-period demand (optional, enter 0.00 if omitted) J : Lower bound on the quantity demanded (optional, enter 0.00 if omitted) K : Quantity demanded in the period before the base period Curve (d) is curve (c) with the reservation price being equal to zero. You define such a demand curve by entering 0.00 as base-period price, 0.00 as the price elasticity, and a lower bound (Q L ). Curve (e) is curve (c) without a lower bound. You define such a demand curve by entering a reservation price, 0.00 as the price elasticity, and 0.00 as lower bound. When the demand curves are horizontal, the three shift variables move them up and down. For example, line 15 in Table 1 indicates that the demand curve for commodity 61 in region 01 is such that in the base-period, at a price of per unit in common currency, the quantity demanded is units. The price elasticity is -0.59, and the elasticities of demand with respect to three shift variables are 0.16, 0.84, and 0.00, respectively. The elasticity with respect to previous-period demand is The lower bound on the quantity demanded is units. The quantity demanded in the period before the base period is units. Worksheet B (Table 2) contains the data that define the supply equations: a base supply quantity; the corresponding base supply price expressed in a common currency (e.g., US$); elasticities with respect to price, up to three other shift variables of your choice, and previous-period supply; a lower bound on the quantity supplied; and an upper bound. You may need to specify the upper bound, while the lower bound is optional (see p. 36). For the base period, you need to provide upper bounds and lower bounds on recovered wastes. For subsequent periods, these bounds are computed by PELPS III as a function of past consumption and recycling parameters (see sections on Recycling and Mathematical Models). 6

10 Figure 1. Demand curves considered in PELPS III. 7

11 Table 2. Data for supply equations. B A B C D E F G H I J K L ****** SUPPLY ****** A : Region number (01 to 99, in ascending order) B : Commodity Number (01 to 99, in ascending order within each region) C : Base period price in common currency D : Rase period quantity supplied at price C E : Price elasticity (>0, enter 0.00 for horizontal supply) F : Elasticity of supply with respect to the first shift variable (optional, enter 0.00 if omitted) G : Elasticity of supply with respect to the second shift variable (optional, enter 0.00 if omitted) H : Elasticity of supply with respect to the third shift variable (optional, enter 0.00 if omitted) I : Elasticity of supply with respect to previous-period supply (optional, enter 0.00 if omitted) J : Lower hound on the quantity supplied (optional. enter 0.00 if omitted) K : Upper bound on the quantity supplied L : Quantity supplied in the period before the base period Similar to the curves for short-term demand, PELPS III allows you to define several types of short-term supply curves (Fig. 2). Curve (a) represents a typical supply function, while curves (b) to (e) are special cases. You define curve (a) with one point ( Q 0, P0) and an elasticity. Curve (b) is curve (a) with an upper bound on the quantity supplied (QU). Curve (c) is curve (b) with an infinite price elasticity. You define such a supply curve by entering a base-period (reservation) price P o, 0.00, as the price elasticity and an upper bound. Curve (d) is curve (c) with the reservation price being equal to zero. You define such a supply curve by entering 0.00 as base-period price, 0.00 as price elasticity, and an upper bound. Curve (e) is curve (c) with no upper bound. You define such a supply curve by entering a reservation price and 0.00 as the price elasticity. If needed, a lower bound on quantity can also be specified in all cases. When the supply curves are horizontal, the three shift variables move them up and down. For example, line 16 in Table 2 shows that the supply curve for commodity 81 in region IO is such that at a price of 7.70 per unit in common currency, the quantity supplied is 100 units. The price elasticity of supply is 1.20, and the elasticities of supply with respect to three shift variables are 1.00, 0.76, and 0.90, respectively. The elasticity with respect to previous-period supply is The upper bound on the quantity supplied is 110 units, and there is no lower bound. The quantity supplied in the previous period is 0.00 units. Moreover, line 19 indicates that the supply curve for recovered waste commodity 85 in region 20 is horizontal (the price elasticity is, but represented by 8

12 Figure 2. Supply curves considered in PELPS III. 9

13 0.00 in PELPS III). In this case, the other elasticities are not applicable and are entered as Given the reservation price of 6.00 per unit in common currency, the quantity supplied is units. The lower and upper bounds on the quantity supplied are and units, respectively. The quantity supplied in the previous period is 5.00 units Manufacture Worksheet C (Table 3) contains the data that define the manufacturing costs in a common currency, called M records, and the manufacturing coefficients, called P records. You must group records of the same type (M or P) and enter all the M records first and all the P records last. Within record type M, the data must be entered in ascending order: (1) by region; (2) by commodity within the same region; (3) by process for the same commodity; and (4) by product mix for the same process. Within record type P, the data must also be entered in ascending order: (1) by region; (2) by input commodity for the same output commodity; (3) by output commodity within the same region; (4) by process for the same input commodity; and (5) by product mix for the same process. Table 3, Data for manufacturing costs and input-output coefficients. C A B C D E F G H I 1 ****** MANUFACTURE ****** 3 A : Record type (two types of records are used, M and P) 4 5 -> Record type M (manufacturing cost) : 6 B : Region number (01 to 99, in ascending order) 7 D : Commodity number (01 to 99, in ascending order within each region) 8 F : Process number (01 to 99, in ascending order within each commodity) 9 G : Input mix number (1 to 9, in ascending order with each process) 10 H : Net manufacturing cost in common currency > Record type P (manufacturing coefficients) : 13 B : Region number (01 to 99, in ascending order) 14 D : Input commodity number (01 to 99, in ascending order within each output commodity) 15 E : Output commodity number (01 to 99, in ascending order within each region) 16 F : Process number (01 to 99, in ascending order within each commodity) 17 G : Input mix number 1 to 9, in ascending order with each process) 18 H : Amount of input commodity per unit of output commodity 20 M M P P P

14 For example, line 20 in Table 3 shows that the unit manufacturing cost of commodity 61 in region 10 using process 11 and input mix 1 is per unit in common currency. Line 24 indicates that 4.16 units of commodity 79 are needed to produce one unit of commodity 61 using process 21 and input mix 2 in region 20. Capacity--1 Worksheet D (Table 4) contains the data that define the net change in global manufacturing capacity (i.e., the total net change in capacity in all regions), from one period to the next, for each manufactured commodity. It is needed only for multiperiod forecasts with the accelerator model of capacity expansion (option 4 of the PELPS III main menu). This global net change in capacity is a linear function of the three previous changes in global production. Net capacity change from t to t+1 = b 1 (production change from t-1 to t) + b 2 (production change from t-2 to t-1) + b 3 (production change from t-3 to t-2) where t is the base period and b 1, b 2, b 3 are expansion parameters in columns E through G. Table 4. Data for expansion of capacity (accelerator model). D A B C D E F G 1 ****** CAPACITY--1 ****** A : Commodity number (01 to 99, in ascending order) B : Production level one period before the base period C : Production level two periods before the base period D : Production level three periods before the base period E,F,G : Expansion parameters For example, line 9 in Table 4 means that the global production of commodity 61, in periods t-1, t-2 and t-3 was 11072, 10069, and 9781 units, respectively. The corresponding expansion parameters of the capacity function are 0.61, 0.35, and 0.14, respectively. Capacity--2 Worksheet E (Table 5) contains the data that define the level and change in manufacturing capacity. For a static model, only the manufacturing capacity in the base period is needed. The other data are required for multiperiods forecasts (option 4 and option 5 of the PELPS III main menu). If option 4 (Run multiperiods - accelerator model) is selected, only data from the first 10 columns (A to J) are needed, and the other columns can be omitted (either left blank or filled with 0.00). Columns I and J contain q and w, the weights of past production and of the q ratio in capacity allocation. They are used to distribute the change in global manufacturing capacity to each region and process (see Eq. [38] in section on Mathematical Models). 11

15 Table 5. Data for cost, physical depreciation, and expansion of capacity (q model). E A B C D E F G H I J K L M N ****** CAPACITY--2 ****** A : Region number (in ascending order) C : Commodity number (in ascending order in each region) E : Process number (01 to 99, in ascending order within each commodity) F : Manufacturing capacity of base period G : Capacity depreciation rate H :Cost of new capacity in common currency (>0) I,J,K,L : Expansion parameters M : Manufacturing capacity one period before the base period N : q ratio in period before the base period (non-negative), enter "-1.00" if not available If option 5 (Run multiperiods - q model) is selected, all 14 columns (A to N) of data are needed. Columns I to L contain b 0, b 1, b 2, and b 3, the expansion parameters used to predict the change in manufacturing capacity by region and process. In the q model, the relative gross change in capacity is a linear function of the current and previous q ratios, and the previous relative gross changes in capacity. That is, gross change in capacity from I to t + 1 = [b 0 + b 1 (q ratio at time t) - b 2 (q ratio at time t-1) + b 3 (relative gross change in capacity from t-1 to t)] * capacity level at t where q is the ratio of the shadow price of capacity to the cost of capacity (see Eq. [42] in Mathematical Models). The data must be entered in ascending order: (1) by region; (2) by commodity; and (3) by process. If there is no depreciation for a process, 0.00 must be entered as the depreciation rate. For example, line 13 in Table 5 shows that the manufacturing capacity of process 11 for commodity 61 in region 10 is 363 units and depreciates at a rate of 5%, per period. The cost of new capacity is 78 per unit in common currency. The expansion parameters (b 0 to b 3) are 0.01, 0.20, -0.11, and 0.54, respectively. The manufacturing capacity and q ratio in the period preceding the base period were 361 units and 0.01, respectively. Recycling (Demand) Worksheet F (Table 6) contains the data that define the fraction of recycled commodity within the total of virgin and recycled commodity. It can be used to force consumption of a commodity to consist of at least a specified fraction of recycled commodity. The data must be entered in ascending order: (1) by region; (2) by virgin commodity; and (3) by recycled commodity. For example, line 8 in Table 6 shows that in region 10, total consumption of commodities 61 and 62 must consist of at least 20% of recycled commodity 62, the rest consisting of the virgin commodity

16 Table 6. Data for commodity recycling constraints on the demand F A B C D E F G H I J K 1 ****** RECYCLING (DEMAND) ****** 3 A : Region number (01 to 99, in ascending order) 4 C : Virgin commodity number (01 to 99, in ascending order within each region) 5 E : Recycled commodity number (01 to 99, in ascending order within each region) 6 F : Fraction of recycled commodity Recycling (Supply) Worksheet G (Table 7) contains the data that constrain the supply and utilization of recovered waste in each region, i.e., the distribution of consumption by region, and the minimum and maximum fractions of recovered waste from a consumed commodity. These data are needed only for multi-period forecasts to impose constraints on the recovery of some commodities. You must provide lower and upper bounds on the supply of the recovered waste for the base period and enter them in Worksheet B. Thereafter, the program will compute them endogenously from past consumption and recovery rates. The data must be entered in ascending order: (1) by region; (2) by recycled commodity; and (3) by consumed commodity. Table 7. Data for commodity recycling constraints on the supply. G A B C D E F G H I J K ****** RECYCLING (SUPPLY) ****** A : Region number (01 to 99, in ascending order) C : Recovered waste number (01 to 99, in ascending order within each region) E : Consumed commodity number (01 to 99, in ascending order within each recovered waste) F : Fraction of commodity consumed in each region G : Minimum fraction of recovered waste from consumed commodity H : Maximum fraction of recovered waste from consumed commodity For example, line 10 in Table 7 shows that 30% of commodity 61 is consumed in region 10. Twenty percent of commodity 61 must be recovered as commodity 85, while at most 40% of commodity 61 can be recovered as commodity 85. Transportation Cost and Tax Worksheet H (Table 8) contains the data that define the transportation costs (in a common currency), and the import and export ad-valorem tax rates. 13

17 Table 8. Data for transportation costs and tax rates. H A B C D E F G H I J K ****** TRANSPORTATION COST AND TAX ****** A : Origin region number (01 to 99) C : Destination region number (01 to 99, in ascending order within each origin) E : Commodity number (01 to 99, in ascending order within each origin-destination) F : Freight cost of shipping one unit of commodity from origin to destination G : Import ad-valorem tax rate H : Export ad-valorem tax rate You must enter the data in ascending order: (1) by origin region; (2) by destination region; and (3) by commodity. If you do not enter a transportation cost between two regions, PELPS III assumes that transportation between these regions is not possible. Transportation costs within a region must be included in the manufacturing costs and in the prices used to position the demand and supply curves. For example, line 10 in Table 8 shows that for shipment of commodity 61 from region 10 to region 01, the cost per unit transported is in common currency, the import ad-valorem tax rate is 10%, and the export ad-valorem tax rate is 6%. Exchange Rate All prices and costs in PELPS III must be expressed in a common currency (e.g., US$). You need to convert the domestic prices and costs to the common currency only for the base period, according to the exchange rates. Thereafter, if you specify exogenous changes in exchange rates, PELPS III will modify prices and costs accordingly. Worksheet I (Table 9) contains the data that define the exchange rates in the base period, expressed as the ratio of each region's currency to the common currency. The data must be entered in ascending order by region, and all demand, supply, and production regions must be included. For example, line 6 in Table 9 shows that the exchange rate between the currency of region 01 and the common currency is That is, in region 01, 1.00 unit of the common currency is equal to 1.17 unit of the regional currency. Exogenous Changes Worksheet J (Table 10) contains most of the data needed to predict changes from one period to the next. The other data are the capacity change parameters in Worksheets D and E. With the data in worksheet J, you can direct PELPS III to simulate changes resulting from 1. shifts of the demand curves (record type D), 2. shifts of the supply curves (record type S) (if parts of the demand (supply) curve are horizontal, then the shift 14

18 Table 9. Data for exchange rates. I A B C D E F G 1 ****** EXCHANGE RATE ****** 3 A : Region number (including demand, supply, and production, 01 to 99) 4 B : Exchange rate (expressed as the ratio of regional currency to common currency) variables move the curve up or down), 3. changes in net manufacturing costs (record type M), 4. new manufacturing coefficients (record type P), 5. new capacities, depreciation rates, and capacity costs (record type K), 6. new fractions of recycled commodities in the consumed commodities (record type C), 7. new coefficients for recovered wastes (record type W), 8. changes in transportation costs, and import and export ad-valorem tax rates (record type T), and 9. changes in exchange rates (record type E) The data are organized by period, headed with the name PERIODt where t (1 t 55) is the period when changes have to be made. There must be no blank lines between PERIODS. PERIOD1 must always be present for multiperiod forecasts, whereas PERIODt (t ³ 2) is optional. If PERIODt is absent, PELPS III assumes that the changes in period t are the same as those in period t-1. Within each PERIOD, each record type is optional. However, you must group records of the same type together and enter them in the following order: D, S, M, P, K, C, W, T, and E. Within each record type, the data must also be entered in the order outlined in Tables 1 through 9. For example, in Table 10, the data in the block PERIOD1 indicate that the periodic changes apply from the base period to period 1. Line 77 indicates that the price elasticity of the demand for commodity 61 in region 01 does not change and that the value of the currency in region 01 relative to the common currency increases by 2% during the period. The first demand-shift variable for commodity 61 in region 01 increases by 1%, the second decreases by 2%, and the third increases by 2% during the period. The growth rate of the lower bound on the demand for commodity 61 in region 01 is 2%. Line 78 shows that the price elasticity of the supply of commodity 81 in region 20 changes to 1.03 during the period. The value of the currency in region 20 relative to the common currency decreases by 1% and there are no changes in the three supply-shift variables. The growth rate of the upper bound on supply, however, is 25%. Line 79 shows that the manufacturing cost in region 10 for commodity 61 using process 11 and input mix 2 increases by 5% in common currency during the period. 15

19 Table 10. Data for exogenous changes in demand, supply, costs, technologies, capacities, depreciation, recycling, taxes, and exchange rates. J A B C D E F G H I J K L M N 1 ****** EXOGENOUS CHANGE ****** 3 A : Data block name (the word PERIOD followed by an integer from 1 to 20) 4 A : Record type (nine types of records are used: D,S,M,P,K,C,W,T,E) 5 6 -> Record type D (shift of the demand curve) : 7 B : Region number 8 D : Commodity number 9 H : Updated price elasticity (< 0), enter 0.00 if no change 10 I : Growth rate in value ofcurrency 11 J : Growth rate ofthe first demand shift variable 12 K : Growth rate ofthe second demand shift variable 13 L : Growth rate ofthe third demand shift variable 14 M : Growth rate of the lower bound on the demanded commodity > Record type S (shift of the supply curve) : 17 B : Region number 18 D : Commodity number 19 H : Updated price elasticity (> 0), enter 0.00 if no change 20 I :Growth rate in value of currency 21 J : Growth rate ofthe first supply shift variable 22 K : Growth rate of the second supply shift variable 23 L : Growth rate ofthe third supply shift variable 24 M : Growth rate of the upper bound on the supplied commodity > Record type M (change of manufacturing cost) : 27 B : Region number 28 D : Commodity number 29 F : Process number 30 G : Input mix number 31 H : Growth rate of real net manufacturing cost in domestic currency > Record type P (new manufacturing coefficients) : 34 B : Region number 35 D : Input commodity number 36 E : Output commodity number 37 F : Process number 38 G : Input mix number 39 H : Updated amount of input per unit of output > Record type K (new capacity, depreciation rate, cost ofcapacity, and parameters) : 42 B : Region number 43 D : Commodity number 44 F : Process number 45 H : Updated manufacturing capacity, enter if no change 46 I : Updated depreciation rate, enter 0.00 if no change 47 J : Updated capacity cost (>0), enter 0.00 if no change 16

20 K,L,M,N: Updated expansion parameters, enter 0.00 if no change -> Record type C (new recycling (demand) coefficient) : B : Region number D : Virgin commodity number F : Recycled commodity number H : Updated fraction of recycled commodity -> Record type W (new recycling (supply) coefficient) : B : Region number D : Recovered waste number F : Consumed commodity number H : Updated fraction of commodity consumed in each region I : Updated minimum fraction of recovered waste from consumed commodity J : Updated maximum fraction of recovered waste from consumed commodity -> Record type T (change of tax rate and transport cost) : B : Origin region number D : Destination region number F : Commodity number H : Change in freight cost I : Change in import ad-valorem tax rate J : Change in export ad-valorem tax rate -> Record type E (change of exchange rate) : B : Region number H : Change in exchange rate PERIOD1 D S M P K C W T E Line 80 shows that the amount of commodity 79 needed to manufacture commodity 61 using process 21 and input mix 2 in region 20 is now 4.12 units. Line 81 shows that the new manufacturing capacity of commodity 61 in region 10 using process 13 is 398 units. This specification overrides the endogenous prediction of capacity by the model. The new depreciation rate and cost of an additional capacity for this process are 1% and in common currency, respectively. There are no changes in the expansion parameters. Line 82 shows that in region 10 the new required fraction of recycled commodity within the total virgin (commodity 61) and recycled (commodity 62) commodities is 25%. 17

21 Line 83 shows that the fraction of commodity 61 consumed in region 20 stays at 0.0 during the period, and the new minimum and maximum fractions of recovered waste commodity 85 from commodity 61 are 30% and 65%, respectively. Line 84 shows that for the shipment of commodity 61 from region 20 to region 03, the freight cost increases by 10% in common currency during the period, the import ad-valorem tax rate does not change, and the export ad-valorem tax increased by 2% (e.g., from 7% to 9%) during the period. Line 85 shows that the change in the exchange rate of region 03 (relative to the common currency) is For example, the exchange rate may have increased from 0.72 to 0.75 since the base period. Saving Data After entering the data, you must save the file before returning to the PELPS III menu. Pressing [Alt] ([Ctrl] if using Lotus for Windows) plus [m] brings a menu to the top of the screen. The menu offers four options: SAVE, PRINT, QUIT, and END. SAVE: saves all the data in the worksheets PRINT: allows you to print the data QUIT: allows you to quit the menu and return to Lotus END: terminates Lotus and returns you to the PELPS III main menu Solving Base- Period Equilibrium Solving MuItiperiod Equilibria PELPS III can be used to solve both static and dynamic competitive equilibria, according to the option selected from the main menu. Option 3 (Run base-period ) computes only the base-period equilibrium using the data saved with option 1 (Edit or input file) selected from the main menu. In PELPS III two capacity expansion models, the accelerator and the q model, are available to predict changes in capacity endogenously (see Mathematical Models). Either capacity model may be selected from the main menu. Both option 4 (Run multiperiods - accelerator model) and option 5 (Run multiperiods - q model) compute a multiperiod forecast and update the data from one period to the next according to the endogenous capacity changes and other exogenous changes saved with option 1 (Edit or create input file) selected from the main menu. Retrieving Data Similar to the data entry phase, PELPS III retrieves equilibrium solutions by means of Lotus Option 6 (Edit output file), calls a Lotus solution file that contains a Lotus macro. Once the file is retrieved, pressing [Atl] (or [Ctrl]) plus [m] brings the main output menu to the top of the screen. The main menu offers eight options: DEMAND, SUPPLY, MANUFACTURING, TRANSPORTATION, CAPACITY, SAVE, QUIT, and END. Each option displays a submenu that provides several choices. 18

22 For DEMAND. Quantity displays the quantities demanded, by region and commodity. Price displays the corresponding prices, by region and commodity. Save allows you to save the data. Quit terminates the submenu and returns you to the main menu. For SUPPLY, Quantity displays the quantities supplied, by region and commodity. Price displays the corresponding prices, by region and commodity. Save allows you to save the data. Quit terminates the submenu and returns you to the main menu. For MANUFACTURING, Process displays the quantities manufactured, by region, commodity, and process. Region displays the quantities manufactured, by region and commodity. Cost displays the manufacturing costs, by region, commodity, and process. Save allows you to save the data. Quit terminates the submenu and returns you to the main menu. For TRANSPORTATION, Quantity displays the quantities transported between regions. Cost displays the transportation costs between regions. Save allows you to save the data. Quit terminates the submenu and returns you to the main menu. For CAPACITY, Process displays the manufacturing capacities, by region, commodity, and process. Region displays the manufacturing capacities, by region and commodity. Shadowprice displays the corresponding shadow prices, by region, commodity, and process. Save allows you to save the data. Quit terminates the submenu and returns you to the main menu. The SAVE option saves a range of the current worksheet in a file of your choice. The current worksheet must be renamed when saving, or the data will be lost. The QUIT option allows you to quit the main menu and return to Lotus The END option terminates Lotus and returns you to the PELPS III main menu. Be sure to save all the data you want to keep before selecting END; otherwise the data will be lost. Application to North American Newsprint Industry This section describes an application of PELPS III that used actual data from the North American newsprint industry. Other applications involving more extensive data have 19

23 been reported by Buongiorno and Gilless (1984), Gilless and Buongiorno (1987), Ince and others (1987), Howard and others (1988), and Ince and others (1993). The main goal of this application was to test the internal dynamics of the model, especially its ability to predict capacity changes accurately. For that purpose, the newsprint industry was chosen, because it has experienced significant technological changes over the past two decades. Historical forecasts were made for the period 1970 to The model predicted demand, supply, production, and trade conditional on income, population, exchange rates, import/export ad-valorem taxes, and wastepaper recovery rates only; capacity was predicted endogenously by the model for the entire period. Regions The demand and supply regions used in this application are shown in Table 11. North America was divided into two demand and five supply regions, and the rest of the world into four net demand regions. The regions that produce the finished product and demand for raw materials and wastepaper are the same as those that supply the finished product. Table 11. Countries and regions used in the application. Demand Canada (01) United States (02) Pacific demand from Canada (03) Atlantic demand from Canada (04) Latin American demand from U.S. (05) Pacific demand from U.S. (07) Note: Numbers in parentheses are the codes in the data file. Supply U.S. North (10) U.S. South (20) U.S. West (30) Canada East (40) Canada West (50) Commodities The commodities used in the application are listed in Table 12. Input commodities are the raw materials and wastepaper grades most used by the North American newsprint industry. Table 12. Commodities used in the application. Raw material Finished product Wastepaper Softwood pulpwood (79) Newsprint (61) Old newspapers (85) Hardwood pulpwood (80) Softwood roundwood (81) Softwood residuals (82) Hardwood roundwood (83) Softwood residuals (84) Softwood chemical market pulp (75) Purchased fuel (89) Electricity (90) Labor (91) Administrative labor (92) Note: Numbers in parentheses are the codes in the data file. 20

24 Processes Table 13 shows the manufacturing processes for newsprint used in the application, based on the different pulping technologies. Each process was defined by an inputoutput coefficient and a cost. Table 13. Processes used in the application. Production region Process R1 (1) 75% groundwood + 25% chemical pulp R2 (2) 90% TMP + 10% chemical pulp (U.S. only) R3 (3) 100% recycled fiber (ONP) R4 (4) 100% TMP or CTMP (Canada only) Note: R can be 1, 2, 3, 4, or 5, respectively, representing each of the five production regions, TMP = thermomechanical pulping, CTMP = chemical thermomechanical pulping, and ONP = old newspapers. Data Results The data used in the application were mainly drawn from the North American Pulp and Paper (NAPAP) Model (Ince and others 1993), whereas the costs and prices were deflated to 1970 dollars. The growth rates in per capita income and population were obtained from the U.S. Department of Commerce ( ). Manufacturing capacities and productions were taken from the American Paper Institute (API) ( a, b) and Lockwood's Directory (1970). Exchange rates were taken from Forest Products Prices of FAO (FAO 1990). In the model, all the supply curves for all raw materials and wastepapers were assumed to be perfectly elastic. The input data file for this model, named PELPS.WK3, is on the enclosed floppy disk. Observed and predicted consumption, production, and manufacturing capacity of newsprint in North America are shown in Figures 3 to 5, for the period Over the entire modeling horizon, predicted consumption and production based on endogenously predicted capacities tracked observed consumption and production reasonably well, although there were substantial errors for individual years. The endogenous predictions of capacity therefore seem adequate. The low forecasts of newsprint capacity (Fig. 5), especially in Canada, did not affect the forecasts of production (Fig. 4). It is also worth noting that given that costs were held constant in this run, much of the growth of the paper industry can be explained by demand forces only. Of course, this situation could change if cost factors were to become sufficiently important as to lead to drastic changes in the price of newsprint. Figures 6 and 7 give the actual and simulated capacity by region for the United States and Canada, respectively. The results indicate that the model predicts the capacity reasonably well (see Canada East), not only at the aggregate level but also at the regional level. Figures 8 to 12 illustrate the simulated technological developments of the newsprint production processes in three U.S. regions and two Canadian regions. Since annual capacity data by process were not readily available, comparisons over the entire simulation period could not be made. However, the 1986 data, which were used as the base year input to the NAPAP model, allowed for an assessment of at least the direction of the technological changes. In fact, during the past two decades, process 2 in the 21