Labor Economics Labor Market Equilibrium Consider the model of labor market equilibrium dismissed in class. As- sume that jobs have all the same 3 hoursfdaty shiFt, so labor supply choices happen only at the extensive margin. That is, workers only need to decide whether to work or not. Also essilme 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 = \"w?" \"There L5 is the measure of workers willing to supply huh-or, to 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- nelug; y = ALE. where A [treasures the productivity, [1,; 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 dierence between revenues and costs: Profit 2 Revenues Costs 11 = pyy wild, where TI is the prot, in is the wage rate, and pa 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 aworker is just high enough to cover his! her costs. in the absence h] Find the value of wage m' and ernploy'ment L' that (:lmrsrzterizes the equilibrium. c) Assume that a, = 1 and \"d = 2. How much does employment grows when A increases by 10%? d] is the number you obtained in part {c} identical to the elasticity of labor demand with respect to A? W'hich one is larger? lWhy? e) The international price of the good that is produced in this labor mar- ket increases from 5 to 9 dollars. Find the change in wages and employment associated with the increase in py. (Hint: That is an 40% increase in pg}. f) Draw a graph of the log labor supply equation and the log labor demand collation. 11] Draw the graph of the lug excess of demand equation [lug Laglug L_.). 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. 1] Now, add to the graph the excess of demand equation associated with and increase in 131, of 30%. 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 a, = [1.5 and CI"; = 2. 6} Assume that the taxe is paid by the rms, not the employees. Does the labor supply schedule shift once the policy is introduced? it so, by how much? h] Continue assuming that the tax is paid by the rms. Does the labor demand schedule shift once the policy is introdlloed? if so, by how much? c) How does the tax affect equilibium wages in this labor market?r cl) Does the. tax changes employment levels? By how much? e} How much of the tax burden is borne by the workers? What is the mechanism through which part of the costs are shifted from the rms to workers? h] Draw the graph of the log [access of demand equation (log Ld log La) before and after the tax is introduced. 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 in both cases. Question 4 Mandated Benets The government decides to force rms to provide all of their employees with health insurance. The current equilibrium wage rate that prevails in the market is SUI dollars a day. The cost of health insurance is 20 dollars per worker per day. The worker's valuation1 or willigness to pay for the health insurance is 15 dollars per day.1 a} Find the change in labor supply associated with this policy. b) Find the change in labor demand associated with this policy