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Lecture 3 National Income Production function Production Function: Y = F(K, L) = Kα L1-α Constant Return to Scale: zY = F(zK, zL) A country as a whole, K and L are constant. Then the supply curve is constant. Production function: scale economy (1) (2) (3) If double the K and the L: Output is doubled constant return to scale Output is less than doubled decreasing return to scale Output is more than doubled increasing return to scale Production function: scale economy Example: STARBUCKS In the 1990s probably increasing return to scale. The company opens a new store every weekday. Since 2008 probably decreasing return to scale. The company has announced 900 store closure in the US. Demand for capital and labor Firms maximize their profits by selecting optimal amount of K and L: Max Profit = Revenue – Labor Costs – Capital Costs = Y -- WL RK = F(K, L) – WL RK α 1-α =K L – WL RK Demand for capital and labor First order conditions: MPK R K 1 L1 R 0 K MPL R 1 K L W 0 L Now we have: MPK = R, MPL = W Discussions #1 MPL = W. If Cobb-Douglas function, 1 K L W At the given level of K, a higher number of workers would lead to a lower wage. Discussion #1 Wage wage MPL, labor demand Quantity of labor demanded Labor Discussions #1 Similarly, MPK = R, we have: K 1 L1 R Since α – 1 < 0, at any given level of L, a higher K would lead to a lower interest rate. Supply is vertical in the whole country Two basic predictions of the model At any given level of L, a higher K would lead to a lower interest rate. At any given level of K, a higher number of workers would lead to a lower wage. Verifying these two predictions are very difficult. Example: the Black Death The Black Death The total number of death world wide are estimated at 75 million. Approximated 25-50 million in Europe, about 30% to 60% of Europe’s population. The effect of the Black Death on wages Labor supply after Labor supply before wage after wage before The Golden Age of British Laborers Wages did not move much long before the Black death. Wages have almost doubled after the Black death. It is still controversial. Example: Mariel Boatlift Began 4/15/1980, and ended 10/31/1980. More than 125,000 Cubans arrived at Southern Florida, mostly in Miami. 50% of them stay in Miami – a 7% increase of the Miami labor market and 20% increase in Cuban working population. Example: Mariel Boatlift The Mariel Boatlift The effect of the Mariel Boatlift on wages Labor supply before Labor supply after wage before wage after The effect of the Mariel Boatlift on wages Not much change in wages for both Cuban workers and for Caucasian workers. Why? The effect of the Mariel Boatlift on wages Labor supply before Labor supply after wage before wage after Demand for labor shift right since capital stock increases Discussion #2: share of income 1 K L W 1 K L L WL 1 Y WL Share of labor is 1-α Share of capital is α. output Share of income Nonwage benefits, such as health insurance etc Demand for goods and services GDP = If NX = 0 GDP = Consumption (C) + Investment (I) + Government Purchase (G) + Net Exports (NX) Consumption (C) + Investment (I) + Government Purchase (G) Consumption Depends on the disposable income: C = C(Y – T) = a + b * (Y – T) Example: C = 250 + 0.75 (Y – T) Marginal propensity to consume: 0.75 On additional dollar, only 75 cents are consumed, the rest is saved. Investment function A higher cost or rental price of capital would lead to a lower investment. Example of investment function: I = I(r) = 1,000 – 50 r. Equilibrium of demand and supply GDP equation: Y = C + I + G = C(Y-T) + I(r) + G Rewrite: Y–C–G=I Supply of loanable fund: Y – C – G = Saving Demand for loanable fund: I(r) Equilibrium of demand and supply Case 1: an increase in government spending, G. Is this true? Case 2: Bush’s cut in capital gains tax Summary Total output is determined by the economy’s quantities of capital and labor (and technology). Y = F(K, L) Competitive firms hire both K and L until its marginal product equals its price. Summary Profit is maximized when MPK = R and MPL = wage. A closed economy’s output is used for: Y=C+I+G In the long run, the equilibrium is reached when saving and investment are equal.