3. Suppose that the bureaucrats who run the Defense Department are budget maximizers. In dealing with Congress, the bureaucrats announce a price p per unit of national defense and Congress gets to choose the level of defense (denoted z). Assume that the Dz curve, which represents Congress' demand for z, is given by Dz = 16 – z. Suppose the true cost per unit of national defense is 3 (i.e., c = 3). Find the socially- optimal level of defense. bureaucrats, and the resulting level of z chosen by Congress. Is national defense underprovided, overprovided, or optimally provided? Is part of the budget wasted by the bureaucrats? If so, how much is wasted? a) Then, find the value of p that is announced by the b) Suppose instead that c = 12. Repeat part (a) for this case.
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- Finn is in charge of decorations for an upcoming festival, and he is planning to decorate withclovers (C) and flags (F). Suppose his preferences over decorations can be represented by theutility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry aboutrestricting to whole-number answers.(a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I.(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the threefirst order conditions.(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: Youdo not need to solve the constrained optimization any more than this.)Assume that the production technology is such that each unit of output requires one unit of labor and that the government has a revenue requirement of one unit of labor. Also assume that there is a single consumer. a. Using a diagram, describe how the optimal tax on the consumption good is determined. Now assume that the consumer has preferences given by U = log(x) + log(10 + ), where x is consumption and is labor supply. b. By maximizing utility subject to the budget constraint qx + w = 0, construct the consumer’s offer curve. c. Treating the equations of the production frontier and the offer curve as a simultaneous system, determine the optimal tax rate.If a new home can be constructed for $150,000, what is the opportunity cost of federal defense spending, measured in terms of private housing? (Assume a defense budget of $600 billion.)
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