Step by step solutions.
1. Consider a physician who receives m. dollars in income per unit of service she provides. The physician values her income, her leisure time, and her patients\" health. The physician may choose to induce I 3 units of services. If the physician induces no services, she prml'ides Q0 :5 units of services. (a) Show the physician's budget set and an indifference curve on a diagram, placing I on the x-axis and the physician's income on the yaxis. Label all axes, intercepts, and curves. [b] Assume the physician prefers to induce a strictly positive number of services. Show her optimal allocation on a new version of the diagram and label it A. Show the indifference curve passing through point A. (c) Interpret the slope of the indifference curve evaluated at point A and state the physician's equilibrium ccmdition. [d] Un another new version of the diagram, display the physician's new budget set if the fee, so, decreases. [e] [In the same diagram as in part (d), display the physician's new optimal allocation at the lower fee, assuming the physician sets I :5 , and label this point B. Carefully display the income and substitution clients on inducement caused by the fee change, assuming their signs are as we assinned in the lectiu'es. 10) You are given the following information about three stocks (X, Y, and Z) in a portfolio: (i) The covariance matrix for each stock with each other stock is given in the following table: X Y Z X 0.040 -0.018 0.016 Y -0.018 0.090 -0.021 Z 0.016 -0.021 0.010 (ii) The weighting of each stock in the portfolio is as follows: Stock Weighting X 30% Y 20% 50% Calculate the variance of this portfolio. (A) 0.0081 (B) 0.0089 0.0123 (D) 0.0902 (E) 0.09442) You are given the following information about a portfolio with four assets. Market Value Covariance of asset's return Asset of Asset with the portfolio return 40,000 0.15 II 20,000 -0.10 III 10,000 0.20 IV 30,000 -0.05 Calculate the standard deviation of the portfolio return. (A) 4.50% (B) 13.2% (C) 20.0% (D) 21.2% (E) 44.7%2 Ricardian Equivalence and Fiscal Policy (30 pts) First consider an economy in which Ricardian equivalence does not hold. A. Suppose the government starts with a balanced budget. Then, there is an increase in government spending, but there is no change in taxes. Show in an IS-LM diagram the effect of this policy on output in the short run. How will the government finance the increase in government spending? (5 pts)1 Consumption and Saving with Uncertain In- come (20 pts) Consider a consumer who lives for three periods: youth, middle age and old age. When young, the consumer earns $20.000 in labor income. Earnings during the middle age are uncertain: there is a 50% chance that the consumer will earn $40.000 and a 50% chance that the consumer carns $100.000. When old, the consumer spends savings accumulated from the previous periods. Assume that inflation, expected inflation, and the real interest rate are equal to zero. Ignore taxes for this problem. A. What is the expected value of lifetime earnings in the middle period of life? Given this number, what is the present discounted value of the expected lifetime labor earnings? If the consumer wishes to maintain constant expected consumption over her lifetime, how much will she consume in each period? How will she save in each period? (6 pts)d. Consider again an increase in government spending combined with an increase in taxes of the same amount. How does this output effect compare to the output effects in parts (a) and (b)? (10 pts)20. Compare the adjustment to medium run equilibrium after a fiscal contraction of a fixed and flexible exchange rate economy. What happens in the short run and during the adjustment to the medium run? Compare your results with the closed economy case
