Question

Problem 3 - Labor Market & Taxes

PROBLEM 3: LABOR MARKET AND TAXES (20 POINTS) Suppose a worker has preferences over consumption and leisure that can be repre- sented by the following utility function: U = ln (C) + In (1) There are 16 hours per day available for leisure (1) and labor (L) (the remaining 8 hours are for sleeping). The hourly wage is w, and assume that the price of each unit of consumption is $1. The only source of income for this worker is the wage. Workers consume all their income, i.e. there is no savings. (4 points) Write down the worker's budget constraint in terms of c and I. (2) (6 points) Find the optimal consumption and labor as a function of w ) (4 points) Now suppose there are 100 workers identical to the one we analyzed. There are also 100 firms, each one with a production function y = VL. Suppose that the price of the firms' output is $1 per unit. Find the labor supply and labor demand curves. (4) (2 points) Find the equilibrium wage and labor. (5) Suppose that the government sets a proportional tax on wages, so for every $1 paid by the firm, the worker receives $(1 – T). (a) (2 points) What is the new labor supply? How has it changed? What's the intuition? (b) (1 points) Find the new equilibrium wage and labor. (c) (1 points) What is the wage paid by firms and the wage taken by workers in the new equilibrium? +1

Answer 1

Q1) l + L = 16

L = 16-l

For BC

Total labor income = total Consumption

Lw= C

C = (16-l)*w

.

2) at eqm, MRS = w

MRS = MUl/MUC

= C/l

So, C/l = w,

C = w*l

So from BC:

w*l = (16-l)*w

2l = 16

l* = 8, so L* = 8

C* = 8w

.

3) Labor supply , Ls = 100*8 = 800 hours

Labor demand is MRPL Curve

MRPL = P*MPL

MPL = dY/dL = .5/√L

So, labor demand Curve ( for one Firm )

w = .5/√L

√L = .5/w

L = .25/w^{​​​​​2}

Aggregate labor demand is horizontal Summation of individual Labor demand Curve

Ld = 100*L

Ld= 25/w^{​​​​​​2}

.

4) at eqm , Ld = Ls

25/w^{​​​​​​2} = 800

w^{​​​​​​2} = 25/800

w* = .176 $

L* = 800

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its mandatory to answer only first Four parts as HOMEWORKLIB RULES policy