Consider an economy where, consumer’s utility function is given as U(C,L)=C-(1/2
ID: 1191884 • Letter: C
Question
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
a) As real wage rises turnover cost will reduce. As real wage rises workers will not be incentivised to leave and hence turnover cost will reduce.
b) As labour increases, their wage rate will reduce and thus turnover cost will become high. As there will be more labour available in the market they will have more incentive to shift and thus turnover cost will be high.
c) Maximize: Profit= Y - turnover cost
(1.6)L - 1/2L2 -3.6/(w/p)
d(profit)/dL = 1.6 - L =0
L=1.6
d) Consumer max: U(C,L) = C - 1/2L2