1) Consider an economy where, consumer’s utility function is given as U(C,L)=C-(

Question

1) Consider an economy where, consumer’s utility function is given as U(C,L)=C-(1/2)L2 . where C is consumption and L is labor. The production technology is Y=(1.6)L-(1/2)L2. The turnover cost per labor is (0.36)/(w/p)

a) What happens to t as real wage increases? Give a clear intuition

b) What happens to t as labor increases? Give a clear intuition

c) Write down the firm’s maximization problem and solve it. Find real wage, labor.

d) Write down consumer maximization problem and solve it. Derive labor supply curve

e) Find real wage, employment, output and unemployment in this economy.

f) Illustrate the solution graphically using Labor Supply / Labor Demand and Production Function diagrams.

Explanation / Answer

Now as the real wage, w/p rises the cost goes up. w/p is the cost of input here.

dy/dl=0 this gives the labour demand

1.6-l=0 or L=1.6

Max u= const – L – (½)L2 gives the labour supply

Du/dl= -1-L=0

At eq, labour demand is equal to the labour supply

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