Labor Economics Labor Market Equilibrium Consider the model of labor market equilibrium dismissed in class. As- sume that jobs have all the same 3 hoursfday shiFt, so labor supply choices happen only at the extensive margin. That is, workers only need to decide whether to work or not. Also assume that the. product produced in this la- bor market is priced at the international markets which makes the demand for the nal good innitely elastic . Thus, changes in the labor market will not affect the price of the good being produced, The number of workers willing to supply labor evolves according to the following labor supply function: L3 = 1.10"" \"There L5 is the measure of workers willing to supply lath-or, tr.- is the wage rate, and 9's is the labor supply elasticity. In the other side of the market, rms face the following production tech- nology: y = ALE. where. A measures the productivity, 1D,; is the number of workers the rm is employing and y is the total number of units of output that is produced. Firms maximize prots. which are the difference between revenues and costs: Profit 2 Revenues -- Costs 11 = pyy wild, where TI is the prot, in is the wage rate, and y is the. prime. of the. product produced in this labor market. This technology of production implies that marginal revenues are given by: orpyA 10 :1 Marginal Revenue = Firms hiring decisions are characterized by the following rule: Continue to increase hiring up to the point that the increase [marginal] in revenue brought by a worker is just high enough to cover his! her costs. in the absence oflahm market taxes, the marginal cost of a worker is given only by hisf'her wage. Thus, we have that firms choice of employment are characterized by; Mrrir'girmi Revenue = rftiryintrt Cost amid _ I Lid-(r T.t Question 2 Labor Market Equilibrium 3} Write down the log labor demand equation. b] Find the value of wage to\" and employment L" that characterizes the equilibrium. c) Assume that as l and 0d 2. How much does employment. grows when A increases by 10%? d] [s the number you obtained in part (c) identical to the elasticity of labor demand with respect to A? Which one is larger? Why? 0) The international price of the good that is produced in this labor mar ket increases item 5 to 9- dollars. Find the change in wages and employment associated with the increase in pg. (Hint: That is an 40% increase in 11y). f] Draw a graph of the log labor supply equation and thel log labor demand equation. h) Draw the graph of the log excess of demand equation (log Ld log L3). Make sure you label the axis. the magnitude of the slope, you identify the height of the intercept. and the exact point that it reaches zero. i] New1 add to the graph the excess of demamtl equatiml associated with and increase in pH of 80%. How much does the height. of the intercept changes? How much does the point in which it. reaches zero move? Question 3 Labor Taxes The government decides to introduce labor taxes. Assume that o\" = [1.5 and (7d 2. a} Assume that the tune is paid by the rms. not the employees. Does the labor supply schedule shift once the policy is introduced? if so: by how much'? b] Continue assuming that the tax is paid by the' Ennis. Does the labor demand schedule shift once the policy is introduced? It" so. by how much? c} How does the tax affect equilihiunl wages in this labor market? d] Does the tax changes employment levels? By how much