M.D. Einstein is considering what she should do for the rest of her life.
She is considering becoming a brain surgeon. She estimates that this would involve tuition of $250,000. However, she reckons that her lifetime earnings would be $5,000,000. Her next best alternative is to go into business with her brother Albert as a partner in his time travel firm. She estimates that this would net her lifetime earnings of $10,000,000. If she decides to become a doctor, what value must she put on the prestige and superior working conditions of being a doctor? What is this called? Suppose tuition rises to $500,000, would her choice of career necessarily change? Why or Why not?
2. Gains from Trade. Consider our fable of the rancher and the farmer. Recall that each allocates 8 hours per day between the production of meat (m) and potatoes (p). Per hour of labour the rancher produces 8 lbs. of meat, while an hour allocated to farming results in the production of 2 lbs. of potatoes. The farmer can produce either 1 lb. of meat or 1 lb. of potatoes per hour. Both the farmer and the rancher have preferences defined over the consumption of meat and potatoes. These preferences can be represented by a utility function. The rancher's preferences are Ur(mr,pr) = mrpr. The farmer's preferences are Uf(mf,pf) = 2ln(mf ) + pf:
(a) Find the production possibilities frontier for the Rancher. Define marginal rate of transformation. What is the marginal rate of transformation of meat for potatoes for the rancher? And also find the production possibilities frontier for the Farmer. What is the marginal rate of transformation of meat for potatoes for the farmer?
(b) If there is no trade, what is the utility maximizing allocation of labourbetween meat and potatoes for the rancher? The corresponding consumption bundle? Utility level achieved? [Hint: What is the objective function? What is the constraint? What are the choice variables? Can you, on one graph, represent both the constraint and preferences? If so what two conditions define the optimal choice, i.e. must hold at the optimal point but don't hold anywhere else?] If there is no trade, what is the utility maximizing allocation of labourbetween meat and potatoes for the farmer? The corresponding consumption bundle? Utility level achieved? [Hint: The marginal utilities for the rancher are MUm= prand MUp= mrand for the farmer, MUm= 2/mf and MUp= 1.]
3. 1. Two tribes inhabit an island where pineapples fall from trees. The population of each tribe has been normalized to 1. A member of Tribe A has the following utility function: U^A(c1, c2) = c1 + c2^(1/2). The marginal utility for first period consumption for A is constant and equal to 1: for second period consumption it is (1/(2c2)^(1/2)). A member of Tribe B has the following utility function: U^B(c1, c2) = c2^(1/2)+ c2. The marginal utility for first period consumption for a B is (1/(2(c1)^(1/2)): for second period consumption it is constant and equal to one. There are two time periods. The endowment of a Atribe member is (m1^A, m2^A). The endowment of a B tribe member is (m1^B, m2^B). Despite their limited diet, the natives are quite sophisticated.
There is a central clearing house where each can post offers of how many period 2 pineapples they will give up for a period 1 pineapple.
(a) How are the posted offers related to the interest rate? What is thebudget constraint of a member of the A tribe? The B tribe?
(b) What is the gross demand for consumption by aAtribe member for pineapples in period 1? In period 2? For a B tribe member in period1? In period 2?
(c) What are the net demands for consumption in period 1 for a member of the B tribe? The A tribe?Suppose that m2^A= 1.0875 and m1^B= 1. Confirm that the equilibriuminterest rate is 0.05. What tribe members are "lenders"? How muchdo they lend? What is the per period consumption of the "borrowers"?The "lenders"?