An economy consists of 4 identical consumers with utility functions over consumption and leisure given by

u(c,l)=64c1/22(24l)2

Consumers have 24 hours in the day to spend on leisure and labor. For each hour they work, they get paid a wage w and they use all of their labor income to purchase a consumption good from the firm. You may assume that the price of the consumption good is equal to 1. There is one firm in the economy with production function

Y=160L2/5

a. Assume each worker is currently working for 16 hours per day and the wage is w=12. Could this consumer increase their utility by working more or less? Explain the economic intuition (based on the marginal rate of substitution)

b. Find the equilibrium wage and total hours worked in this economy.

c. The government imposes a minimum wage of $15. Calculate labor supply and labor demand and show what is happening on a graph of labor supply and labor demand

d. An increase in immigration causes the number of consumers in the economy to increase to 6 (the new consumers still have identical utility). What effect does this have on the equilibrium wage and hours worked? Show the effect on a graph.