- 2 14 Points Property And Power Assume The Same Functions U And F As In The Previous Exercise Suppose That The Land Is 1 (101.06 KiB) Viewed 35 times
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- 2 14 Points Property And Power Assume The Same Functions U And F As In The Previous Exercise Suppose That The Land Is 3 (65.88 KiB) Viewed 35 times
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- 2 14 Points Property And Power Assume The Same Functions U And F As In The Previous Exercise Suppose That The Land Is 5 (101.06 KiB) Viewed 35 times
1 [4 points) Consumption Versus Leisure Angela chooses how many hours H € (0.16) a day to work; the remaining hours L = 16 - H is her leisure. Angela's preference is described by the utility function U(L, C) = C + 32L - L?, where C € (0.+00) is the money she has to spend daily and we will refer to C as consumption. (a) (0.25 point) Give a formula for Angela's marginal utility of leisure MU.(L,C). (b) (0.25 point/ Give a formula for Angela's marginal utility of consumption MUC(L.C). (C) (0.25 point) Give a formula for Angela's marginal rate of substitution of leisure for consumption MRS(L,C) = -A LC MU(1.0). Marginal rate of substitution is the slope of the indifference curve passing through the point (L,C), and it tells us how much consumption Angela is willing to give up to gain another hour of leisure (when ap- proximating her indifference curve by its tangent at the point (L.C)). (d) (1 point/ Suppose that Angela has a part-time job that pays her a constant hourly wage w = 16, so that C = wH. How many hours H a day will Angela choose to work to maximize her utility, and how much would her consumption C be? (Recall that the optimal point is characterize by that the slope MRS(L,C) at that point equals to the slope -w of the budget line.) Illustrate the situation graphically (L on the 2-axis, C on the y-axis, display the budget line and the indifference curve passing through the solution). (e) (1 point) How much would the wage have to be for Angela to choose to work all 16
2 14 points) Property and Power Assume the same functions U and f as in the previous exercise. Suppose that the land is now owned by Bruno who rents it to Angela. Thus, what is being produced is now split between the consumption CA of Angela and the consumption of Bruno CB, i.e. CA+Cb = f(H), where H is hours that Angela works on the land (Bruno does not work). Angela's preference is given by her utility function U(L, CA), and Bruno maximizes his consumption CB. (a) (1 point) Before we discuss how the consumption C = f(H) is split between Angela and Bruno, consider the following allocations: x1 = (LP.C.) = (8, 150), X² = (L?,CA) = (8.200), X3 = (L.) = (10, 190). What can you say about Pareto dominance among these allocations? Recall that allocation XPareto dominates allocation X if and only if U(LCA) > U(D,CA) and at the same time C > C) (where y = f(H') - C). Illustrate graphically, showing the indifference curves passing through these allocations. (b) [1 point/ Suppose that Angela is Bruno's slave. Bruno decides how many hours Angela has to work (H) and how much she gets to consume (CA). The only thing that constrains Bruno's cruelty are Angela's biological survival limits, which are U(L, CA) > U. = 300. Show in a graph the technically feasible set of points (L, CA). (e) (1 point) How many hours H will Bruno want Angela to work to maximize his own consumption CB? In other words, which of the points from the technically feasible set is optimal for Bruno? Recall that such a point is characterized by the first order condition that Angela's marginal rate of substitution MRS(L.CA) equal to the marginal rate of transformation MRT(L), and that CA is such that U(L, CA) = U. Illustrate the situation graphically. (d) (1 point) Consider next, that Angela has an option to escape Bruno's farm to a nearby monastery where she would be provided with consumption CA = 100 in exchange for H = 4 hours of work. Show in a graph the set of all the economically feasible allocations, i.e. the allocations such that Angela voluntarily continues working at Bruno's farm instead of choosing the outside option of leaving to the monastery.