Question

# Suppose u=u(C,L)=4/5 ln⁡(C)+1/5 ln⁡(L), where C = consumption goods, L = the number of days taken...

Suppose u=u(C,L)=4/5 ln⁡(C)+1/5 ln⁡(L), where C = consumption goods, L = the number of days taken for leisure such that L=365-N, where N = the number of days worked at the nominal daily wage rate of \$W. The government collects tax on wage income at the marginal rate of t%. The nominal price of consumption goods is \$P. Further assume that the consumer-worker is endowed with \$a of cash gift.

a) Write down the consumer-worker's budget constraint.

b) Write down the marginal benefit of leisure relative to consumption.

c) Write down the marginal cost of leisure relative to consumption.

d) Based on your answers to parts b and c, write down the consumer-worker's decision rule.

e) Derive the labor supply equation. (Hint: Subsititute the budget constraint into the decision rule in part d, and solve the result for L in terms of P, W, a and t.)

f) Based on your answer to part e, if the government increase the income tax rate t, labor supply {INCREASES, DECREASES, STAYS THE SAME} as the labor supply curve shifts {RIGHTWARD, LEFTWARD, NOWHERE} . Please help! Thank you!