1 - SaBHBBI ^ m v > x S EMPIRICAL MACRO PRODUC TION FUNCTIONS SOME METHODOLOGICAL COMMENTS by Sören Wibe Umeå Economic Studies No. 153 UNIVERSITY OF UMEÅ 1985 ISSN
2 - 1 - EMPIRICAL MACRO PR ODUCTION FUNCTIONS - SOME tcthodological COMMENTS I INTRODUCTION The possibilities of analyzinq production technologies and technological progress have increased considerably over the last years. New functional forms for cost and production functions, with little or no restrictions on technology have been introduced, and modern computers have made it possible to use advanced statistical methods at low cost. Following this trend, it has become increasingly popular to work with macro (industry) production functions without any restrictions on returns to scale and homotheticity. One such example was recently published in this journal (Rao and Preston, 1984) and we shall use that particular study to illustrate the theme of this paper. In their study Rao and Preston estimated industrial cost functions for the Canadian economy using the translog formulation. They did not impose any restrictions on the elasticity of scale (ELS) and their results (table 6, p. 103) show an ELS significantly different from unity (< 0.95 or > 1.05) in 23 of 34 cases. Nor were any restrictions regardinq homotheticy imposed, and their findings indicated that the production function was non-homothetic for all industries. Despite these results I would like to argue that a macro production function of the kind estimated by Rao and Preston should always be assumed to be homothetic and to have constant returns to scale. A non-homothetic macro production function with non-constant returns to scale presents problems of theoretical consistency and of interpretion. 1 The purpose of this paper is to demonstrate this. Since the matter is of some importance for the empirical study of production, I present a fairly detailed argument and some, already well informed, readers might find this article somewhat descriptive. 1 It should be pointed out, however, that our remarks refer to the definitions used by Rao and Preston, i.e. where returns to scale and homotheticity are defined with respect to total (industry) output. (See also section IV of this paper).
3 II THE PROBLEMS OF THEORETICAL CONSISTENCY The conditions for the existence of macro production functions have been the subject of much discussion among economists. The core problem is that a given amount of inputs in macro can be associated with many different micro distributions (to different firms in the industry) and that, consequently, many different output levels might be associated with a given set of inputs. In order to avoid this problem of indeterminness, it is customary to use the same optimality defintion as for the micro production function. Accordingly, a macro production function is defined as the relation which maximizes total output, given a set of input. Associated with each macro production function is a least cost function relating input prices and output level (for the industry) to the cost level for the industry as a whole. Formally, there is then a close analogy between micro and macro cost and production functions. Nevertheless, there is one very important difference. In order to secure the existence of a micro cost function it is sufficient to assume a cost minimizing firm. However, this is not enough for the existence of a macro cost function. On the macro level we must also introduce a condition that ensures that total output is efficiently distributed to the individual firms. It is easily shown (and intuitively obvious) that total cost is minimized if, and O only if, the marginal cost is equal for all firms. This can of course happen under many different real world situations, but two possibilities are simple and obvious: 2 Short summaries (with detailed references) can be found in Muyskens (1979) and in Wibe (1980, Ch. II). See also Green (1964) 3 We do not complicate our discussion with second-order conditions.
4 - 3 - (i) firms are operatinq in a competitive economy and/or (ii) all firm functions are equal and with constant returns to scale If firms are operatinq in a competitive economy, then all adjust the rate of production until marqinal cost equals price, and, since the price is the same for all firms, we know that all marqinal costs are equal. If, on the other hand, all firms have the same constant returns to scale production function, then all firms have the same marginal cost irrespective of output level. 1 * If condition (ii) is valid, it is quite obvious that the macro production function has constant returns. We drop this case for the moment and concentrate on the other possibility: the economy is a competitive economy. It is now necessary to consider two possibilities referring to different time periods of production: the short run and the lonq run. The short run is conventionally defined as a situation where the capital stock is fixed and the long run is, since Marsh.all, defined as C a situation with all factors variable. If capital is fixed then it no longer represents a choice variable and it is, therefore, excluded from the production function formulation (and its price from the cost function). With this remark we abandon the short run case and consider only the long run situation. 4 Of course it is possible to construct situations with firm-equal marqinal costs other thfein those above, but these situations are, of necessity, complicated and if they are not explicitly stated, it seems reasonable to disreqard them. 5 Aqain, we can define other types of production functions or define short and lonq run differently, but it is then a reasonable demand that such unconventional definitions, if used, should be explicitly explained.
5 - 4 - If all factors are variable and if we are dealing with a competitive economy, there is a simple equation for the ELS, the elasticity of scale, which applies both to micro and macro level. 6 ELS = COSTS/REVENUE (1) However, in a competitive economy the entry of new firms and the scrapping of old will ensure that quantities and prices adjust until zero profits are obtained by all firms. Accordingly, a competitive economy with all factors variable will always end up with ELS = 1. Constant returns to scale is an equilibrium condition for a competi-.tive economy. We are now in a position where we can compare our results with the methods used by Rao and Preston. They begin by assuming the existence of a production function for each industrial sector relating gross output to the services of capital, labour, energy and material (p. 93). They then write:... "If we assume that factor prices and output are exogenous and that firms are cost-minimizers, the theory of duality implies that associated with the production function is a cost function of the form. C i * «P Ki' P Li' P Ei' P Mi- B i' T > where C^ is the total cost of the i-th industry and P ^> P ^ are the prices of capital, labour, energy and material... and T is a time trend - a proxy for technical change" (p. 93). 6 By definition ELS = E where Q is output and v^ inputs. Also i i we know that dq/dv^ = P^/P where P^ is the price of input i and P the price of the product. Combining these yields ELS = (Z P v. )/P Q = COSTS/REVENUE: i
6 - 5 - The decisive mistake is hidden in this statement. The theory of duality is a micro economic theory derived from the theory of the firm and it does not state anything about macro cost and production functions. In order to establish the macro cost function (or rather to arque why observable price-cost points should belong to a macro cost function) we must change the assumption of cost-minimizing firms to an n assumption of a competitive environment. After making this alteration we can use the macro economic version of the theory of duality! Capital is treated in the same way as all the other factors. It is assumed for example that the quantity factor demand can be derived using Shepard's lemma (p. 94). Thus, we must conclude that capital (like labour enerqy and material) is variable. Finally, Rao and Preston assume (on p. 95) that all factor cost-shares add up to one, which implies that capital, labour, enerqy and material are all existing (economic) factors of production. In all, we can conclude that the (implicit) assumptions made by Rao and Preston (which are the same as those made in large number of similar studies) implie that they are analyzing long run fupctions in a competitive economy. As argued earlier we should always assume ELS = 1 for such functions or give very specific reasons why this is not done, otherwise the model is theoretically inconsistent. Another point worthy of attention in this connection is the following: If we assume marginal pricing (e.g. by using Shepard's lemma) then it is obvious that an implicit decision on scale properties is taken once we have decided on the ratio of costs to revenue (see eq. (1)). If for example, we assume that all revenue (= sales) can be distributed to different cost-items, this actually means that we have assumed that ELS =1.1 have not been able to discover whether this is the case for Rao and Preston, but I strongly suspect that it is. In Rao (1981) where some comments on the data base are qiven, it is stated that... "Capital costs are calculated residually" (p. 193). The crucial 7 Which of course includes cost minimizinq firms.
7 - 6 - question is of course "Residually from what?" If they are calculated residually from total sales then Rao and Preston have already assumed ELS = 1. 8 The above discussion has hinted at the inconsistencies in not assuming ELS = 1 for the kind of macro production functions calculated by Rao and Preston. Firstly, it is implied by assuming that observable data points are points on a macro cost function, that an assumption of a competitive economy has been made. It is then inconsistent not to assume ELS = 1 since this logically follows from the competitive assumption. Secondly, it is evident from (1) that an implicit decision as to the value of ELS is taken before any calculation is made, once the relationship of costs to revenues has been decided. As a third point, we could add that theoretical long run macro production fune- Q tions all have constant returns to scale. The conclusion is clear: If we want a macro function with non-constant returns to scale, then we must assume (i) that we are dealing only with a short-run function - a function where not all factors are variable, or we must assume (i i) that the market is not characterized by perfect competition. The homothetic property of macro functions follows directly once we admit that ELS = 1 for all output levels My suspicion that this is the case emerges from the statistical result where ELS was fairly close to one in almost all cases. 9 See Johansen (1972), pp , Bentzel and Johansson (1959), pp See Fersund (1974), proposition 1, p. 109.
8 - 7 - II PROBLEMS OF INTERPRETATION It might be argued that computations with non-homothetic and scaleunrestricted macro production functions are interesting despite the theoretical inconsistencies. For example, a finding that the elasticity of scale is siqnificantly different from unity could indicate serious imbalances in the sector or something of that nature. However, the opposite is true: Only by introducing the restriction ELS = 1, and by assuming that the function is homothetic can we obtain truly reliable and clear empirical information. We beqin by recalling that we work with a long run function in a competitive environment. We then ask for the precise meaning of a macro function with non-constant returns to scale. For instance, how shall we interpret Rao and Preston's result that ELS = 0.67 for the wood industry? Formally, it means that an increase of all factors by 1 % will increase industrial output by 0.67 %. However, this result is absurd since we must assume that the old technology can (at least) be copied, i.e. that an increase in all factors by 1 % should be able to produce at least 1 % more output. Thus, unless we are willing to assume indivisibilities (which is a strange assumption in a macro context) we must assume that ELS > 1 in order to give the result a reasonable interpretation. However, an elasticity of scale (strictly) greater than one also presents problems of interpretation. Formally, this means that a 1 % increase in factor input will produce more than 1 % output, i.e. that the marginal productivity is greater than the average productivity. In other words we are dealing with some sort of putty-clay technology where the marginal ("new") firms are more efficient than older ones. Again, we end up with conclusions which run contrary to the model's assumptions. Returns to scale is in itself a micro concept, even if it can be applied to macro conditions (in some cases). At the micro level, it simply means that the relation between input and output varies with the size of a plant. This is a well known fact of technology, thus returns to scale, as an economic measure, has a solid background in a
9 - 8 - technical reality. This is not the case for macro returns to scale. There is no technical reason what so ever why total industrial output should be associated with scale advantages or disadvantages once we assume a long run production model without indivisibilities. The technical reason for economics of scale is to be found on the plant level, and no scale effect can ever arise if we just change the number of plants in operation. This confusion between plant and industry are illustrated by the following sentence from Rao and Preston. They write:..."the finding of slightly diminishing or constant returns to scale is contrary to the popular view that increasing returns to scale exist in the manufacturing sector. These results do not suggest that there are vast untapped gains to be made from product specialization". (ibid, footnote 23, p. 103). But a macro function with a constant ELS is not contrary to the "popular view" of increasing returns to scale. The "popular view" refers to plant size and means simply that larger plants produce more efficiently. This fact is perfectly in accordance with an observation that changes in total industrial output are associated with a proportionate change in total input. Exactly the same arguments which are used for returns to scale could be repeated for homotheticity. For instance, the findings by Rao and Preston that "output growth is capital using" (p. 99) means formally that marginal macro technology is different from average technology, i.e. that an extra plant should use more capital than all the others. Again, this is contrary to the model's assumption. Another statistically important point is that an assumption of nonhomotheticity and non-constant returns to scale distorts the measurement of technological progress and technological bias. Since outputs in most industries grow over time, there is generally a strong positive correlation between output and time. And since time is used as a
10 - 9 - proxy for technical change, we have a correlation between output growth and technical progress. Given this correlation there is a risk that the efficiency gains made through technical progress are estimated as gains attributable to advantages of scale. The authors themselves are aware of this risk (Rao and Preston, 1984, note 24, p. 103). Inspection of their results (table 6) also shows that in all cases where the ELS was much greater than 1, then the rate of technical progress was negative (!) (7 cases) or zero (2 cases). The correlation between output growth and time is also a probable source of confusion between technological bias and non-homotheticity. A technological bias, for instance in the labour-saving direction, is easily registred as a labour-saving scale bias and vice versa. Inspection of the results shows that a factor-saving bias with regard to technological progress was connected with a factor-using tendency with regard to scale in 2/3 of the reported cases (40 out of 60 cases). Our conclusion is clear: far from adding anything empirically interesting, the introduction of non-homothecity and non-constant returns to scale destroys the reliability of the relevant empirical information. IV CONCLUDING REMARKS The enormous growth of new functional forms for cost and production functions, and the growth of cheap computer based statistical packages, has caused a rapid growth in the number of empirical production studies. However, the increased availability of empirical technigues is also a potential danger. The main element in our understanding of nature and society is theory, and figures are meaningful only in the light of well defined theoretical concepts. One of the purposes of this paper has been to demonstrate this danger. More specifically, it has been argued that a macro production function should be assumed to be homothetic and to have constant returns to scale. The real reason for this is that the guestion of homotheticity and returns to scale is a question of plant technology. At the macro level, the technological issue is not a comparison between output
11 levels, but between plants. If technology should change with output, this must be due to a technology difference between plants. 11 However, there is no room for such difference in a long run production model. Returns to scale and homotheticity are micro concepts in a long run model. Accordingly, if they are to be studied statistically, they should be represented by a micro measure. The simplest and most natural measure here is average plant size. By using this, instead of total industrial output, as a measure of scale, the analysis of Rao and Preston (and others) could be repeated. The model would thus be theoretically consistent and the empirical results far more relevant and interesting. 11 In short run macro scale since plants functions we can speak of a macro returns to are of different productive efficiency.
12 -11- REFERENCES Bentzel, R. and Ö. Johansson. Om ho mogenitet i produktionsfunktioner. Ekonomisk Tidskrift 1959, Fersund, F. Studies in the Neoclassical Theory of Production. Memorandum from Institute of Economics, University of Oslo, Feb. 4, Green, H.A.3. Aggregation in Economic Analysis. Princeton, Johansen, L. Production Functions. North-Holland, Amsterdam, Muyskens, I. Aggregation of Putty-Clay Production Functions. Ph.D. thesis, University of Groningen, Groningen, Rao, P.S. Factor Prices and Labour Productivity in the Canadian Manufacturing Industries. Empirical Economics, Vol. 6, 1981, Rao, P.S. and R.S. Preston. Inter-Factor Substitution, Economics of Scale and Technical Change. Evidence from Canadian Industries. Empirical Economics, Vol. 9, 1984, Wibe, S. Teknik och aggregering i produktionsteorin. Ph.D. thesis. Department of Economics, University of Umeå, 1980.
1 Integrating the Input Market and the Output Market when Teaching Introductory Economics May 2015 Clark G. Ross Frontis Johnston Professor of Economics Davidson College Box 7022 Davidson, NC 28035-7022
Discussion of Capital Injection, Monetary Policy, and Financial Accelerators Karl Walentin Sveriges Riksbank 1. Background This paper is part of the large literature that takes as its starting point the
Working Paper No 7/07 Pricing of on-line advertising: Pay-per-view or pay-per-click? by Kenneth Fjell SNF project no 303 Konvergens mellom IT, medier og telekommunikasjon: Konkurranse- og mediepolitiske
385 356 PART FOUR Capital Budgeting a large number of NPV estimates that we summarize by calculating the average value and some measure of how spread out the different possibilities are. For example, it
19. Transfer Prices A. The Transfer Price Problem A.1 What is a Transfer Price? 19.1 When there is a international transaction between say two divisions of a multinational enterprise that has establishments
A Review of the Literature of Real Business Cycle theory By Student E XXXXXXX Abstract: The following paper reviews five articles concerning Real Business Cycle theory. First, the review compares the various
Chapter 4 Consumption, Saving, and Investment Chapter Outline Consumption and Saving Investment Goods Market Equilibrium 4-2 Consumption and Saving The importance of consumption and saving Desired consumption:
Chapter 8 Inflation This chapter examines the causes and consequences of inflation. Sections 8.1 and 8.2 relate inflation to money supply and demand. Although the presentation differs somewhat from that
Factor Markets Problem 1 (APT 93, P2) Two goods, coffee and cream, are complements. Due to a natural disaster in Brazil that drastically reduces the supply of coffee in the world market the price of coffee
Chapter 12: Cost Curves 12.1: Introduction In chapter 11 we found how to minimise the cost of producing any given level of output. This enables us to find the cheapest cost of producing any given level
I. Learning Objectives In this chapter students will learn: A. The significance of resource pricing. B. How the marginal revenue productivity of a resource relates to a firm s demand for that resource.
Managerial Economics 1 is the application of Economic theory to managerial practice. 1. Economic Management 2. Managerial Economics 3. Economic Practice 4. Managerial Theory 2 Managerial Economics relates
1 The background Smith on Natural Wages and Profits (Chapters VIII and IX of The Wealth of Nations 1 ) Allin Cottrell When Smith begins work on the specifics of natural wages and profits, he has already
Advertising Sotiris Georganas February 2013 Sotiris Georganas () Advertising February 2013 1 / 32 Outline 1 Introduction 2 Main questions about advertising 3 How does advertising work? 4 Persuasive advertising
ECO364 - International Trade Chapter 2 - Ricardo Christian Dippel University of Toronto Summer 2009 Christian Dippel (University of Toronto) ECO364 - International Trade Summer 2009 1 / 73 : The Ricardian
Notes 10: An Equation Based Model of the Macroeconomy In this note, I am going to provide a simple mathematical framework for 8 of the 9 major curves in our class (excluding only the labor supply curve).
Perfect Competition There are two concepts of competition normally used in Economics: 1. The manner or process in which firms compete with one another for market share. 2. A description of a particular
Chapter 3 A Classical Economic Model what determines the economy s total output/income how the prices of the factors of production are determined how total income is distributed what determines the demand
These notes provided by Laura Lamb are intended to complement class lectures. The notes are based on chapter 11 of Microeconomics and Behaviour 2 nd Canadian Edition by Frank and Parker (2004). Chapter
ECO 352 Spring 2010 Precepts Weeks 1, 2 Feb. 1, 8 REVIEW OF MICROECONOMICS Concepts to be reviewed Budget constraint: graphical and algebraic representation Preferences, indifference curves. Utility function
1 I S L 8 0 5 U Y G U L A M A L I İ K T İ S A T _ U Y G U L A M A ( 4 ) _ 9 K a s ı m 2 0 1 2 CEVAPLAR 1. Conigan Box Company produces cardboard boxes that are sold in bundles of 1000 boxes. The market
Asymmetry and the Cost of Capital Javier García Sánchez, IAE Business School Lorenzo Preve, IAE Business School Virginia Sarria Allende, IAE Business School Abstract The expected cost of capital is a crucial
Measuring Unilateral Market Power in Wholesale Electricity Markets: The California Market, 1998 2000 By FRANK A. WOLAK* * Department of Economics, Stanford University, Stanford, CA 94305-6072, and NBER
Macroeconomics Lecture 1: The Solow Growth Model Richard G. Pierse 1 Introduction One of the most important long-run issues in macroeconomics is understanding growth. Why do economies grow and what determines
RELEVANT TO ACCA QUALIFICATION PAPER F1 / FOUNDATIONS IN ACCOUNTANCY PAPER FAB Introduction to microeconomics The new Paper F1/FAB, Accountant in Business carried over many subjects from its Paper F1 predecessor,
Monopolistic Competition, Oligopoly, and maybe some Game Theory Now that we have considered the extremes in market structure in the form of perfect competition and monopoly, we turn to market structures
Rafal Borkowski, Hipoteczna 18/22 m. 8, 91-337 Lodz, POLAND, E-mail: firstname.lastname@example.org Krzysztof M. Ostaszewski, Actuarial Program Director, Illinois State University, Normal, IL 61790-4520, U.S.A., e-mail:
1 CHAPTER 11. AN OVEVIEW OF THE BANK OF ENGLAND QUARTERLY MODEL OF THE (BEQM) This model is the main tool in the suite of models employed by the staff and the Monetary Policy Committee (MPC) in the construction
Chapter 14 Competitive Market Equilibrium We have spent the bulk of our time up to now developing relationships between economic variables and the behavior of agents such as consumers, workers and producers.
Chapter 5 Real business cycles 5.1 Real business cycles The most well known paper in the Real Business Cycles (RBC) literature is Kydland and Prescott (1982). That paper introduces both a specific theory
The Real Business Cycle model Spring 2013 1 Historical introduction Modern business cycle theory really got started with Great Depression Keynes: The General Theory of Employment, Interest and Money Keynesian
+ Price Elasticity of Demand + n Elasticity = measure the responsiveness of one variable to changes in another variable. n Price elasticity of demand measures the responsiveness of demand to changes in
Chapter 21: The Discounted Utility Model 21.1: Introduction This is an important chapter in that it introduces, and explores the implications of, an empirically relevant utility function representing intertemporal
The Journal of Prediction Markets (2007) 1, 61 73 EFFICIENCY IN BETTING MARKETS: EVIDENCE FROM ENGLISH FOOTBALL Bruno Deschamps and Olivier Gergaud University of Bath University of Reims We analyze the
HW #7: Solutions QUESTIONS FOR REVIEW 8. Assume the marginal cost of production is greater than the average variable cost. Can you determine whether the average variable cost is increasing or decreasing?
Controlling Inflation: Applying Rational Expectations to Latin America Matthew Hughart, Mary Washington College This paper examines the relationship between inflation and unemployment in three Latin American
Regret and Rejoicing Effects on Mixed Insurance * Yoichiro Fujii, Osaka Sangyo University Mahito Okura, Doshisha Women s College of Liberal Arts Yusuke Osaki, Osaka Sangyo University + Abstract This papers
Volatility, Productivity Correlations and Measures of International Consumption Risk Sharing. Ergys Islamaj June 2014 Abstract This paper investigates how output volatility and productivity correlations
Chapter 6 We recall that perfect competition was theorised as a market structure where both consumers and firms were price takers. The behaviour of the firm in such circumstances was described in the Chapter
CHAPTER 8 PROFIT MAXIMIZATION AND COMPETITIVE SUPPLY TEACHING NOTES This chapter begins by explaining what we mean by a competitive market and why it makes sense to assume that firms try to maximize profit.
Economics Proposal for CORE 2014 due by February 1, 2013 ------------------------------------------------------------------------------------------------------ Executive Summary: The Economics Curriculum
Specific Factors and Heckscher-Ohlin: An Intertemporal Blend Ronald W. Jones University of Rochester Two of the standard workhorse models used in discussing competitive equilibrium in the pure theory of
KRUGMAN MODEL - MONOPOLISTIC COMPETITION Overview: This model uses economies of scale, differentiated products and heterogenous preferences to explain intraindustry trade. The essence of the model is as
Unit 5.3: Perfect Competition Michael Malcolm June 18, 2011 1 Market Structures Economists usually talk about four market structures. From most competitive to least competitive, they are: perfect competition,
C H A P T E R E L E V E N P e r f e c t c o m p e t i t i o n Assume for the moment that you have completed your business training and that you are working for some consulting firm. The first assignment
Intermediate Microeconomics Economics 435/735 Fall 0 Answers for Practice Problem Set, Chapters 6-8 Chapter 6. Suppose a chair manufacturer is producing in the short run (with its existing plant and euipment).
Subsidies in oligopoly markets: a welfare comparison between symmetric and asymmetric costs Stephen F. Hamilton and Rickard Sandin Oligopolistic industries generally produce less than is socially desirable.
ECON 312: Oligopolisitic Competition 1 Industrial Organization Oligopolistic Competition Both the monopoly and the perfectly competitive market structure has in common is that neither has to concern itself
Chapter 8 Production Technology and Costs 8.1 Economic Costs and Economic Profit 1) Accountants include costs as part of a firm's costs, while economists include costs. A) explicit; no explicit B) implicit;
(Perfect) Competition (Perfect) Competition The model of perfect competition is based on the following assumptions: (Perfect) Competition The model of perfect competition is based on the following assumptions:
Gains from Trade: The Role of Composition Wyatt Brooks University of Notre Dame Pau Pujolas McMaster University February, 2015 Abstract In this paper we use production and trade data to measure gains from
Effects of electricity price volatility and covariance on the firm s investment decisions and long-run demand for electricity C. Brandon (email@example.com) Carnegie Mellon University, Pittsburgh,
Applied Economics Letters, 2003, 10, 857 861 Hedonic prices for crude oil Z. WANG Department of Economics, Monash University, PO Box 197, Caulfield East, Victoria 3145, Australia Email: Zhongmin.Wang@BusEco.monash.edu.au
Agenda The IS LM Model, Part 2 Asset Market Equilibrium The LM Curve 13-1 13-2 The demand for money is the quantity of money people want to hold in their portfolios. The demand for money depends on expected
1) Suppose the Fed reduces the money supply by 5 percent. a) What happens to the aggregate demand curve? If the Fed reduces the money supply, the aggregate demand curve shifts down. This result is based
Additional Exercises The Ricardian Model 1 Suppose Country A and Country B can both produce bicycles and computers Assume also that Country A s opportunity cost of a computer is three bicycles, and Country
Schooling, Political Participation, and the Economy Online Supplementary Appendix: Not for Publication) Filipe R. Campante Davin Chor July 200 Abstract In this online appendix, we present the proofs for
19 : Theory of Production 1 Recap from last session Long Run Production Analysis Return to Scale Isoquants, Isocost Choice of input combination Expansion path Economic Region of Production Session Outline
Chapter 11 PERFECT COMPETITION Key Concepts FIGURE 11.1 Perfectly Competitive Firm s Demand Curve Competition Perfect competition is an industry with many firms, each selling an identical good; many buyers;
EC201 Intermediate Macroeconomics EC201 Intermediate Macroeconomics Lecture 10: Aggregate Demand and Aggregate Supply I Lecture Outline: - how to derive the aggregate demand from the IS-LM model; - a preliminary
Utah State University DigitalCommons@USU All Graduate Plan B and other Reports Graduate Studies 2012 How Are Interest Rates Affecting Household Consumption and Savings? Lacy Christensen Utah State University
Monopoly Problem 1 (APT 93, P3) A single airline provides service from City A to City B. a) Explain how the airline will determine the number of passengers it will carry and the price it will charge. b)
Goldwasser AP Microeconomics Chapter 13 Perfect Competition and the Supply Curve BEFORE YOU READ THE CHAPTER Summary This chapter develops the model of perfect competition and then uses this model to discuss
WSG9 7/7/03 4:34 PM Page 131 9 Market Structure: Monopolistic Competition OVERVIEW Although the conditions necessary for the existence of perfect competitive and monopoly are unlikely to be found in the
Economics 165 Winter 2002 Problem Set #2 Problem 1: Consider the monopolistic competition model. Say we are looking at sailboat producers. Each producer has fixed costs of 10 million and marginal costs
Constrained optimisation roblems in economics typically involve maximising some quantity, such as utility or profit, subject to a constraint for example income. We shall therefore need techniques for solving
Fiscal Studies (1997) vol. 18, no. 3, pp. 93 30 Inequality, Mobility and Income Distribution Comparisons JOHN CREEDY * Abstract his paper examines the relationship between the cross-sectional and lifetime
Chapter 4 Technological Progress and Economic Growth 4.1 Introduction Technical progress is defined as new, and better ways of doing things, and new techniques for using scarce resources more productively.
The Case Against Intellectual Property Michele Boldrin and David K. Levine University of Minnesota and UCLA 1 Introduction Conventional wisdom: Presence of strong intellectual property right spurs innovation
The Elasticity of Taxable Income: A Non-Technical Summary John Creedy The University of Melbourne Abstract This paper provides a non-technical summary of the concept of the elasticity of taxable income,
Labour Demand Labour is a factor of production, and labour, like other factors, such as capital (machinery, etc) are demanded by firms for production purposes. The quantity of labour demanded depends on
Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically
Increasing Returns and Economic Geography Paul Krugman JPE,1991 March 4, 2010 Paul Krugman (JPE,1991) Increasing Returns March 4, 2010 1 / 18 Introduction Krugman claims that the study of economic outcomes
c December 24, 2016, Christopher D. Carroll Endogenous Generic Analysis of Endogenous Growth Models The neoclassical theory of economic growth, as formulated by Solow (1956), and Cass (1965)-Koopmans (1965),
Where are we? To do today: finish the derivation of the demand curve using indifference curves Go on then to chapter Production and Cost Utility and indifference curves The point is to find where on the
The Labour Market: Demand and Supply Learning Objectives Understand that the demand for a factor of production such as labour is derived from the demand for the product and that it will be influenced by
Lecture 2. Marginal Functions, Average Functions, Elasticity, the Marginal Principle, and Constrained Optimization 2.1. Introduction Suppose that an economic relationship can be described by a real-valued
Sensitivity Analysis 3 We have already been introduced to sensitivity analysis in Chapter via the geometry of a simple example. We saw that the values of the decision variables and those of the slack and
Chapter 4 The Theory y of the Firm under Per erfect Competition In the previous chapter, we studied concepts related to a firm s production function and cost curves The focus of this chapter is different
Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually
Trinity College Dublin Instructor: Martin Paredes Department of Economics Michaelmas Term 006 Industrial Organization Answer Key to Assignment # 1 1. What are the economic costs of operating the restaurant
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized