Representative consumers have the utility function U(C,L s ) = ln(C) + ln(1- L s

Question

Representative consumers have the utility function U(C,Ls ) = ln(C) + ln(1- Ls )

Representative consumers have labor endowment of 1. So Ls must be less than 1

Representative firm’s production function is Y(Ld )=4 Ld

There is perfect competition in the markets (so price and wages are taken as given by firms and consumers)

a) Write down profit function of the firm

b) Solve for the firms maximization problem and find the labor demand

c) Write down the budget constraint of the representative consumer

d) Write down the maximization problem of the representative consumer and find labor supply

e) Write down the market clearing conditions

f) Solve for equilibrium labor supply and labor demand

g) Solve for equilibrium goods demanded and goods supplied

h) Solve for equilibrium price and wage

Explanation / Answer

a.

Profit of the firm = revenue – Cost

Profit of the firm = Y – (W/p)*Ld

Profit of the firm =4Ld – (W/p)*Ld

Profit of the firm =(4Ld – (W/P)*Ld)

b.

Solve for the firms maximization problem and find the labor demand

Profit of the firm =(4Ld – (W/P)*Ld) ------------------------(1)

Differentiating eq. 1 w.r.t. Ld and equating them to zero

Dp/DLd = 4 – (w/P) = 0

(w/P) = 4

W = 4P                          or W/P = 4

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