Question

3. The Firm's Problem and Taxes (30 points total). Suppose the representative firm has a production function given by Y = 2K" , where =K=4. The real wage equals 2. Suppose the firm is subject to a revenue lax. Specifically, the firm has to pay $l to the government for each Sl worth of output sold alternatively, pay units to the government for each unit of output sold). (a) (5 points) Write down the firm's maximization problem.

Answer 1

A) nominal profit= p*Y-p*real wage* N - p*Y*t

Real profit=y - real wage -yt

Profit=8√N -2N-8*t*√N

Profit=8√N(1-t) - 2N

B) optimal condition of firm,

MPL*1-t=real wage

MPL=4/√N

(4-4t)/√N=2

C) labour demand;(4-4t)/√N=2

√N=2-2t

N=(2-2t)^2

N=4-4t2-8t

Output;y=8√N=8√(2-2t)^2=8(2-2t)=16-16t

Profit=16-16t(1-t)-2(4-4t2-8t)=16-16t+16t2-8+8t2+16t

Profit=8-8t2

Tax Increase, decreases labour demand .

D)profit Maximizing problem;,

Gross Profit=8√N-2N

Net profit( after tax)=8√N*t- 2*N*t

Optimal condition,( now optimal condition remain same as without tax because tax is levied on profit,so objective is Maximizing profit)

MPL=real wage

4/√N=2

2=√N

N=4