Classical/neoclassical model - UITS

1 Classical/neoclassical model Graduate Macroeconomics I. ECON 309 -- Cunningham A Simple neoclassical model Assumptions z Market economy with private property. z Markets are fully competitive. z All variables in the model are either endogenous, or exogenous and supplied. z Initially, there is no government. z Except when indicated, the general equilibrium assumptions obtain. z Two kinds of individual agents exist in this economy firms and households. Agents FIRMS: -produce commodities -supply the commodities at the market price -demand labor, paying the market wage -undertake investment HOUSEHOLDS: -Consume (purchase) commodities (at market prices). -Supply labor at a wage -Save neoclassical model , Continued z No agent suffers money illusion; therefore, the analysis is real, with the price level determined separately from the relative prices.. z Firms and households are each homogeneous. Therefore, we collapse the analysis to that of a single representative firm and a representative household, and aggregate to form the firm and household sectors.

2 Z The commodities are also homogeneous, so that we consider a single commodity whose real quantity is Y.. (Usually, we use y for real output, and Y for nominal. z Therefore, the price of the commodity is the price level, P.. z There are three (3) markets in this economy: - Commodity Market - Labor Market - Capital Market (Loanable Funds or Bond Market). neoclassical model , Continued z The nominal wage is w, and the real wage is therefore w/P.. z The rate of interest (the price of capital) is r. (The convention is to use i for the nominal interest rate and r . for the real interest rate. z There are three factors of production capital (K), labor (N), and land (L). These factors are perfectly homogeneous. , all workers look the same (have the same productivity and skills). At times, we assume that some of these factors, L and sometimes K, are fixed. That is, K=K0 and L=L0. This leads to Y = AF(K,L0,N) = AF(K,N) = F(K,N). = AF(K0,L0,N) = AF(N) = F(N). neoclassical model , Continued z Firms are technically efficient.))

3 That is, they produce the maximum output possible from the factors. z Diminishing returns apply to production. Mathematically, this is equivalent to: F F. > 0, > 0 Positive marginal returns to labor and capital. N K. 2F 2F. < 0, 2 < 0 Diminishing marginal returns to labor and capital. N 2. K. 2F 2F Capital and labor marginal productivities are = =0. N K K N independent of one another. Production Function Y Y=F(N*,K). Y3. Y2. Y1. The level of employment has already been established in the labor market. K. K1 K2 K3. Production Function: MPK. Y. Y3. B Y=F(N*,K). Y2. Y1. A The slope of the tangent at point A is the MPK at point A. The slope of the tangent at point B is the MPK at point B. K. K1 K2 K3. Production Function: MPN. Y. Y=F(N,K*). B. Y3. Y2 The slope of the tangent at point A is Y1. the MPN at point A. A. The slope of the tangent at point B is the MPN at point B. N. N1 N2 N3. Capital Change Y. Y=F(N,K2). Y2. Y=F(N,K1). Y1. N. N1. Technology Change Y. Y=A2F(N,K*).

4 Y2. Y=A1F(N,K*). Y1. N. N1. The model The Firm Profit Maximizes We begin with a representative firm: The firm's profit function is = PY wN Pr(K K0). Maximize profit: Assume A=1, Y=F(N,K) and construct expressions for change in profit relative to changes in employment (N) and capital (K) and set to zero. Solve. First Order Conditions: d = P(dY) w dN = 0 The firm is profit- maximizing when these conditions are met. d = P(dY) Pr dK = 0. ---------------------- dY/dN = w/P Marginal Product of Labor = Real Wage dY/dK = r Marginal Product of Capital = Real Interest Rate Theory of Distribution z This is a theory of distribution. It explains how output is shared by the various agents. Workers (households) are paid according to what they actually contribute to the production process (on the margin). Capital is also paid according to its contribution (on the margin). z This implies that for the real wage of workers to rise (their real buying power to increase) while prices remain stable, real labor productivity must also rise.

5 Labor Demand If we differentiate the first result with respect to real wages (w/P), we have by the chain rule: 2 F N. =1. N ( P ). 2 w divide by the first term: N 1. = 2. (P ) F. w N 2. but by assumption 2 F. <0. N 2. therefore N. < 0 Labor demand slopes downward. (P ). w Implications w/P. Cet. Par., labor demand by firms rises as real wages fall. Labor demand slopes Nd downward. N. r We can show similarly, cet. par., that investment demand by firms rises as interest rates I fall. The investment curve S, I slopes downward. Households Optimize The representative household maximizes utility. Since utility is assumed to result from consumption only, this turns out to be the same as maximize real income. If utility were maximized in a multi-period model , we would analyze the intertemporal optimization choices associated with electing whether to consume now or later, with the disutility of foregoing current consumption offset by interest income on savings. In this single-period model , the intertemporal aspects of the decision making process are captured by the interest rate.

6 This amounts to the abstinence theory of interest espoused by William Nassau Senior in the 1800s. People are thought to prefer current to future consumption, but a higher interest rate makes it more likely for households to choose to postpone consumption in favor of higher real consumption later as a result of interest income. Micro Analysis of Labor Supply W/P W/P Ns 4 4. 3 U3 3. 2 U2 2. U1. 15 16 18 24 6 8 9. hours of leisure hours of work Households Optimizing Income Household income is given as the sum of wage income, interest income, and distributed profits: PY = wN s + iB d + . or w s Bd . Y = N +i +. P P P. B d Recall that Y=C+S, S = . This is a budget constraint; it P. forces the household to balance income and expenditures. Households Optimize (2). Y w Differentiating with respect to Ns yields: =. N s P. If we proceed with the optimization as in the firm case, we (+ ). find: }. s w . N =N . s P . (+ ). }. And S = S (r ) since i/P = r. ( ). }. which implies (from the budget constraint): C = C (r ).

7 Implications r S Cet. Par., saving by households increases as interest rates rise. The saving curve slopes S, I upward. w/P. Ns Cet. Par., labor supply by households rise as real wages rise. Labor supply slopes upward. N. Capital Market Summary r S. r* S*, I*, r* K*. I. S*, I* S, I. I(r*) = S(r*). Here r* is the Wicksellian natural rate of interest, S* and I* are equilibrium savings and investment. In this market claims on capital are traded. Capital Market/Bond Market/Loanable Funds Market r S PB Bs r* PB*. I Bd B* B. S*, I* S, I. Note: Investment (I) is the Saving = supply of funds = bond demand change in the amount (stock) Investment = demand for funds = bond supply of capital. Production Function Y Y=AF(N,K*). Y* The level of capital has already been established in the capital market. N. N*. K* = K0 + K = K0 + I - . Labor Market Summary w/P Voluntary Ns Unemployment (w/P)* (w/P)*, N*. Nd N* N.. d w . *.. s w . *.. N = N = N *. P P . Involuntary Unemployment w/P. Ns N s > Nd (w/P)1 Results in involuntary (w/P)* unemployment Nd N1 N* N2 N.

8 Effect of an Increase in Labor Productivity 1. Labor is more productive. w/p Ns 2. Firms increase (w/p)2. demand for labor. (w/p)1. 3. Employment Nd2. increasese and Nd1. wages are bid N. N1 N2. upward. The effects of skill-biased technical change on wage inequality Personal Income Tax Cut 1. The same real N s1. wage is more w/p attractive to N s2. workers. (w/p)1. 2. Labor supply (w/p)2. increases. 3. Employment increases and Nd wages fall. N1 N2 N. 4. Unemployment Rate falls. Classical Real Sector LRAS. P. 4. 1 r S. r* S*, I*, r*, K*. Y* Y. I. S*, I* S, I. 2 Y=F(N*,K*). w/P Y. Ns Y*. 3. (w/P)* (w/P)*, N*. Nd N* N. N* N. Classical Dichotomy P LRAS. w/P Y. Y* r S. r*. Ns I. Nd N Y=F(N,K) S*,I* S,I. Increase in Labor Productivity P LRAS1. LRAS2. +. w/P Y r + S. + r*. Ns I. Nd1. Nd2 N Y=F(N,K) S*,I* S,I. Supply-side Tax Cut P LRAS1. LRAS2. - w/P Y. + r S. + r*. N s1 Nd I. N s2 N Y=F(N,K) S*,I* S,I. Quantity Theory of Money z The theory: for a given level of output, the price level is proportional to the quantity of money.

9 Z This theory is made explicit in the equation of exchange. Equation of Exchange (1). Fisher's transactions model : MVT = PT T. M = the stock of money in circulation (money supply). VT = the circular velocity of transactions (velocity of money); also called the transactions velocity of circulation PT T. VT =. M. PT = Price index for goods traded T = Real value of transactions Velocity of Circulation z The velocity of money is the average number of times per period (year) a unit of currency (dollar). is used in making a transaction. z The velocity of money is governed by the nature and sophistication of the payments system in the society, and therefore changes slowly over time. z The velocity of money is not related to any of the other variables in the model , so can be considered exogenous or fixed with respect to these equations. Equation of Exchange (2). Income (output) model : MVY = PY. M = the stock of money in circulation (money supply). VY = the circular velocity of income (velocity of money); also called the income velocity of circulation PY.

10 VY =. M. P = Price index for goods traded Y = Real Income (GDP). Velocity of Money z The income velocity of money is the average number of times per period (year) a unit of currency (dollar) is spent in producing GDP (total economic activity). z As with the transactions velocity of money: z The income velocity of money is governed by the nature and sophistication of the payments system in the society, and therefore changes slowly over time. z The income velocity of money is not related to any of the other variables in the model , so can be considered exogenous or fixed with respect to these equations. Equation of Exchange (3). Cambridge cash-balances model : M = kPY. M = the stock of money in circulation (money supply). k = Cambridge cash-balances constant -- the average holding period of each unit of the currency (dollar). 1. k=. V. P = Price index for goods traded Y = Real Income (GDP). Eq. Of Exchange (3) Continued z The Cambridge model is closer to a modern theory of money demand.