Week 4 Seminar Material: A Closed Economy One Period Macroeconomic Model

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1 PC IN ECONOMICS 2005 Week 4 Seminar Material: A Closed Economy One Period Macroeconomic Model Questions for Review 1. Why is it useful to study a closed-economy model? A closed economy is a model of single country that has no interaction with the rest of the world--- it does not trade with other countries. It is easier to work with, and if we first understand how a closed economy works, much of the economic intuition we build up for the closed-economy case carries over to an open economy. That is, opening the economy does not change most of the properties we found in a closed economy model. So our strategy for modelling building is to start with a simple model and then add complications. Also, the closed economy is the correct model of the world. What are the two critical criteria to evaluate a model whether it is good or bad? Simplicity (parsimony) and explanatory power, which could be trade-off. (See Occam's Razor: It forms the basis of methodological reductionism, also called the principle of parsimony or law of economy. In its simplest form, Occam's Razor states that one should make no more assumptions than needed. Shave off unnecessary assumptions in explanation.) 2. Can the government run a deficit in the one-period model? Why or why not? No. Government budget deficit is G-T, where G is government expenditures and T is taxes. In a one period model, all agents (including the government) spend whatever they have because there is no future to save. Moreover, government cannot borrow from somewhere else to spend more than she taxes since there will be no future to repay its debt. Therefore we need G=T in a oneperiod model. 3. What are the four conditions that a competitive equilibrium must satisfy for this model? i) Consumer optimization Representative consumer choses C and N s to maximize utility Max U(C,N s ) s.t C=wN s + -T ii) Firm optimization Representative firm choses N d to maximize profits Max (Y,N d ) s.t Y=zF(K,N d ) iii) abor market clears Demand for labor = Supply of abor N d =N s iv) Government budget constraint is satisfied G=T

2 4. Explain the difference between the first and second welfare theorems. Why is each useful? The 1st theorem of welfare economics: Under certain conditions, every competitive equilibrium is Pareto optimal. That is, the outcome of competitive market is economically efficient. It ensures that free market system working through competition results in a good outcome (resource allocation). However, this may not necessarily be a socially desirable allocation. The 2nd theorem of welfare economics: Under certain conditions, every Pareto-optimal allocation can be a competitive equilibrium for some set of initial endowments. It allows us to analyse directly Pareto optima (through Social Planner assumption) with assurance that these outcomes are also competitive equilibria, esp., when it is difficult to work with competitive equilibrium. 5. Give three reasons that equilibrium might not be Pareto optimal. i) Externalities Firms may produce more or less than the socially optimal level ii) Distorting taxes Proportional income tax example (MRS < MPN) iii) Monopoly power May lead to underproduction Problems 1. Suppose that the government decides to reduce taxes. In the model used in this chapter, determine the effects this will have on aggregate output, consumption, employment, and the real wage, and explain your results. C C 2 B C 1 A -G 2 -G 1 l 1 l 2 h A reduction in taxes implies

3 A reduction in government expenditure (G=T by gov. budget constraint) Consumer s disposable income increases (Y d =Y-T) Initial equilibrium is at point A PPF shifts to the right, new equilibrium at B Consumption and leisure increases (positive income effect, both normal goods) Employment reduces (since leisure increases) Output reduces (since employment reduces) Real wages increase (employment reduces, marginal product of labour rises when employment falls, green line is steeper) 2. Faroffland is an island state that does not trade with the rest of the world. Unfortunately, the island of Faroffland is actively volcanic. A volcanic eruption destroys part of Faroffland s capital stock, though there is no loss of life (the representative consumer survives). a. Determine the effects on aggregate output, consumption, employment, and the real wage, with reference to income and substitution effects, and explain your results. Y=zF(K,N d ) An erosion of capital stock will lower aggregate output at all levels of labour proportionately depending on the form of the production function Y Y Y 1 * Y 2 * Production function N Output as a function of leisure

4 C Y 1 *-G Y 2 * -G M K PPF 3 N PPF 2 PPF 1 -G Aggregate output will decrease Consumption decreases, the change in leisure (thus employment) depends on the magnitude of income and substitution effect. M to N total effect M to K substitution effect (lower consumption, increase leisure) K to N income effect (both consumption and leisure goes down) Real wage (slope of PPF) goes down regardless of the magnitude of income and substitution effect (the output produced by per unit of labor lowers as a result of erosion of capital stock which has the effect of reducing MP. Therefore, demand for labor goes down and so does the real wages) b. Describe another type of event that would cause a decrease in a nation s capital stock. Interpret your results in terms of this other type of event. A war. c. Do you think that changes in the capital stock are a likely cause of business cycles? Explain, with reference to your answers in parts (a) and (b) and the key business cycle facts described in Chapter 3. Key business cycle facts: Consumption is procyclical (consistent with our model) Employment is procyclical (depends on the magnitudes of income and substitution effect) Real wage is procyclical (consistent with our model) 3. Suppose that the government treats government expenditures G as a policy instrument, and suppose that the policy goal of the government is to stabilize consumption for the representative consumer. That is, whenever z changes in the economy, the government observes this, and changes G in such a way that C is the same before and after the change in z. Now, suppose that z falls.

5 a. In what direction will the government need to change G in order to stabilize C when z falls? Government should reduce G When z falls production function shifts down proportionately (from PPF 1 to PPF 2 ) MP decreases Output decreases Consumption decreases When government reduces G (from PPF 2 to PPF 3 ), taxes go down because we have G=T owering taxes will increase the disposable income of the consumer Consumption is a normal good; therefore, an increase in disposable income will increase consumption. Note that PPF 3 has a smaller y intercept than the PPF 1. This is due to the fact that the reduction in total factor productivity caused a fall in marginal product of labour and even with full capacity; lower output can be attained now. C PPF 1 IC 1 IC 2 C * PPF 3 M J Z PPF 2 N (0,0) -G h -G b. If the government stabilizes C when z falls, show that employment and aggregate output must fall, and that the representative consumer must be better off than before the

6 decrease in z. Explain your results. You will need to show the income and substitution effects involved to solve the problem. When government reduces G Substitution effect : consumption lowers, leisure increase Income effect: both consumption and leisure increase, both are normal goods Since leisure increases, employment falls Since employment falls, output must also fall Real wages rise, (firms lowers employment in response to a rise in wages) Representative consumer is better off (consumption and labour increased). However, employment is lower now.