Purpose: Achieve a good command of endowment, labor supply and intertemporal choice. Truelfalsefuncertain 1. 5" Given an endowment (when), ceteris paribus if the prices of 1:1 and x; double then the budget line remains unchanged. As long as leisure is a normal or superior good, paying higher hourly wages for working overtime can increase the amount of optimal leisure. Assume there are two goods. If the price of one good increases ceteris paribus, then all net sellers of that good remain net sellers, but some net buyers of the other good may switch to net sellers. The Federal Reserve Bank can affect the marginal rate of substitution of consumers. If there are n goods and a consumer is a net seller of n 1 of them, then an increase of 10% in all prices will make this consumer better off. The labor Supply model is awed because it assumes work is bad, and many people seem to like working. Problem 1. Ted is an eight-year-old boy who loves Pokemon cards and Lego minigures. His father found a website where Ted can trade cards for minigures (and vice versa) at a rate of one card for two minigures. His preferences are represented by u(x1,xg) = xlixf", where m stands for cards and 3:; stands for minifigures. Assume both goods are perfectly divisible. a. Draw the budget constraint assuming Ted has an endowment of 5 cards and 6 minigures, i.e. (wliwl) = (596) b. Given the budget constraint in part a, nd Ted's optimal bundle. c. Is Ted a net buyer of net seller of cards? What about minigures? d. Assume Ted trades to get to the optimal bundle in part b. Imagine Ted visits the website two months later and learns each minifigure can now be traded for two cards. Draw the new budget constraint. Notice that the bundle in part b is Ted's new endowment. Given the new budget constraint in part d, nd the new optimal bundle. Relative to the optimal bundle in part b, is Ted now a net buyer or net seller of cards? What about minigures? '7"? Problem 2. Jeffrey's preferences are described by u(R,C) = Racb, where R denotes leisure and C denotes consumption. Assume the price of consumption is 1, the wage rate is w, non-labor income is f, and Jeffrey has a total time available (for either work or leisure) equal to E. a. Draw the budget line and write its equation. b. Find the demand function for R' in terms of w, C and R. Hint: imagine you extend the budget line until it crosses the leisure axis. Use the shortcut seen in class to nd demands when we have Cobb-Douglas preferences. c. Find the labor supply function, that is, R R' as a function of w, C and R. Is it positively or negatively related to w? Hint: dene L" = f? R". Compute 6L*f6w and check its sign. d. Assume leisure is defined in hours. What is the value of w that will make Jeffery work eight hours? Express it in terms of C and R. e. Humans are living longer and longer. If we dene I? in terms of years of productive life, we can say that E is becoming larger. What is the effect of a greater 1? on optimal leisure and consumption, ceteris paribus? f. Two presidential candidates are proposing alternative policies to increase labor income. Candidate A is proposing a cut in social programs that would decrease C by 20%. Candidate B is proposing a tax cut that would increase w by 20%. Which one would more effective? Explain your answer. Problem 3. Andy and Bob were born at the same time but followed different career paths. Andy became a neurosurgeon. Bob became a great mixed-martial arts fighter. Assume Andy's total earnings before age 40 are $500,000, whereas Bob's are 10 million dollars. The situation will flip as they grow old. Andy's total earnings after age 40 will be 10.5 million dollars, whereas Bob's will be $525,000. For simplicity, assume life has two periods: before and after age 40. Consumption in the first period is denoted by ci, and consumption in the second period is denoted by c2. Andy and Bob have the same preferences, described by u(c1,C2) = c1' c2. a. Assuming an interest rate of 5% across periods, show that the lifetime earnings of Andy and Bob have the exact same net present value. b. Given their endowments m, and my (i.e., their earnings in each period) and an interest rate of 5%, find the optimal bundles of Andy and Bob. In period 1, who would be a saver? Who would be a borrower? c. Draw a graph showing the endowments and the budget lines of Andy and Bob, as well as their optimal bundles. d. Assume now that the interest rate increases to 10%. Find the new optimal bundles for Andy and Bob. Who benefits from this change? Who doesn't? Explain how you arrive to your answer. e. Financial institutions usually charge a spread when they lend money. In other words, there are two interest rates: the passive rate paid to savers, and the active rate charged to borrowers. Assume a passive rate of 5% and an active rate of 7.5%. Find the new optimal bundle for Andy. f. Assume a new bank is offering loans at an active rate of 5% but it charges a "lending fee" defined as a fixed amount in dollars. What would be the fee that would leave Andy's purchasing power constant at the optimal bundle in part e? g. Assuming the new bank charges an interest rate of 5% and the lending fee you found in part f, what would be Andy's optimal bundle? Would he be better off than when the active rate is 7.5% but there is no lending fee? Explain in your own words why or why not