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# Ymirs budget line

1. Ymir Larson farms near Niffleheim, Minnesota. He works 80 hours a week. He can either growrutabagas or raise pigs. Every hour that he spends growing rutabagas gives him \$2 of income thisyear. Every hour that he spends raising pigs this year will add \$4 to his income next year. In fact,next years weekly income will be 100 + 4H dollars where H is the number of hours he spendsraising pigs this year. Ymirs utility function is U(c1, c2) = min{c1, c2}, where c1 and c2 are hisconsumption expenditures this year and next year. Ymir doesnt believe in banks and will neitherlend money nor borrow money.a. Draw Ymirs budget line for current and future consumption, labeling key points on it.b. How many hours a week will he choose to spend raising pigs?c. How much money will he spend per week on consumption in each year?2. Clancy has \$1,200. He plans to bet on a boxing match between Sullivan and Flanagan. For \$4, hecan buy a coupon that pays \$10 if Sullivan wins and nothing otherwise. For \$6 he can buy acoupon that will pay \$10 if Flanagan wins and nothing otherwise. Clancy doesnt agree with theseodds. He thinks that the two fighters each have a probability of of winning. If he is anexpected utility maximizer who tries to maximize the expected value of lnW, where lnW is thenatural log of his wealth, howmany coupons would it be rational for him to buy?3. For each of the following production functions, draw a diagram showing the general shape of itscorresponding isoquant. Comment on the ease at which labor and capital can be substituted forone another relative to the other two production functions.a. Q = K + L.b. Q = K0.5L0.5.c. Q = min(K, L).4. A competitive firm has a production function described as follows. Weekly output is the squareroot of the minimum of the number of units of capital and the number of units of labor employedper week. Suppose that in the short run this firm must use 16 units of capital but can vary itsamount of labor freely.a. Write down a formula that describes the marginal product of labor in the short run as a functionof the amount of labor used. (Be careful at the boundaries.)b. If the wage is w = \$1 and the price of output is p = \$4, how much labor will the firm demand inthe short run?c. What if w = \$1 and p = \$10?d. Write down an equation for the firms short-run demand for labor as a function of w and p.5. The cost function c(w1, w2, y) of a firm gives the cost of producing y units of output when thewage of factor 1 is w1 and the wage of factor 2 is w2. Find the cost functions for the followingfirms:a. A firm with production function f (x1, x2) =min{2×1, 3×2}b. A firm with production function f (x1, x2) = 2×1 +3x2c. A firm with production function f (x1, x2) =max{2×1, 3×2}

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