Consider the case of a monopsonist who is the only employer in an isolated town. There are are 100 individuals who live in the town, and each has a utility function

U (C, L) = 0.75 ln C + 0.25 lnL

where L is leisure and C is consumption. The price of consumption is normalized to 1. Each individual has a non-labor income of $10. Each person's time endowment is 16. The price of monopsonist's good is $20. The monopsonist only uses labor in production and has the production technology

f (E) = E.

Question 3.1 Solve worker's problem and find the labor supply curve for the town. Express the labor supply curve in terms of total worker-hours. HINT: By solving worker's optimization problem, you will find the labor supply curve for one worker. Since there are 100 identical workers, you will need to multiply hours by 100 to get the supply curve for the town.

Question 3.2 Find the wage, labor demanded and output by the monopsonist.

Question 3.3 How much labor will the monopsonist demand if with a minimum wage of $5?

Question 3.4 How about a minimum wage of $25?