Assume that Alice and Bob get enjoyment from two things: aggregate consumption of goods,

, and hours of leisure, . They have the same utility function = (, ). Both must decide

how many hours they would like to work. The price of consumption goods is given by = 1.

Alice's wage in her job is 20 dollars per hour and Bob's is 40 dollars per hour. Assume that each has 80 hours available each week that can be either spent on working or leisure, and they do not have any income other than their labor earnings.

(a) What are Alice's and Bob's budget constraints respectively?

(b) We observe that Alice chooses to work 40 hours per week and Bob works 50 hours per week. On a graph, use their budget constraints and indifference curves to illustrate the optimal choice of both consumers. Please label the optimal consumptions, labor supply, and leisure hours on the graph.

(c) The comparison of Alice's and Bob's choices shows that when the wage increases from $20 to $40 per hour the labor supply increases from 40 hours to 50 hours. Can you come up with an estimate of the elasticity of labor supply with respect to the wage using this observation? Is the labor supply elastic or inelastic?

(d) If the government levy a payroll tax of 20% on Bob, how does it affect Bob's budget constraint? Would the tax increase or decrease Bob's labor supply? Explain.

(e) Assume that the government introduces a welfare program to help Alice, which includes a lump-sum transfer of $400 each week with a phaseout rate of 25%, i.e. Alice gets $400 transfer each week if she does not have any labor earning but for each dollar she earns the transfer decreases by 25 cents. How does such a program affect Alice's budget constraint? Would it increase or decrease Alice's labor supply? Explain.