businessss.. this is acomplete questuion

Consider a Cobb-Douglas production function Y = AKL1with = 0.6 and A = 1.5. Assume that the savings rate is s = 0.04, the population growth rate is n = 0.02 and the depreciation rate is = 0.05. 1. Using the Solow-Swan model, compute the steady state values of k, y, and of consumption per person c. 2. Find the level of s that maximizes c, and the corresponding steady state value of k.

3. Does the model allow for long-term growth? 4. Suppose the World Bank wants to help this country by either (i) directly increasing k, or (ii) by doubling A. How would each of these actions affect the steady state values of y and c and the transition dynamics of k?

Instructions. Each question is 33 points. Good Luck! 1. Let P be the set of lotteries over {a, b, c} x {L. M. R). In which of the following pairs of games the players' preferences over P are the same? (a) L M R L M R 2,-2 1,1 -3.7 a 12,-1 5.0 -3,2 1,10 0.4 0.4 5,3 3,1 3,1 -2,1 1,7 -1,-5 -1,0 5,2 1,-2 (b) L M R L M R 1.2 7,0 4,-1 1,5 7,1 4-1 6.1 2.2 8.4 6.3 2,4 8.8 3,-1 9,2 5.0 9,5 5,1 2. Let P be the set of all lotteries p = (Pr, py; p.) on a set C = {r, y, z } of consequences. Below, you are given pairs of indifference sets on P. For each pair, check whether the indifference sets belong to a preference relation that has a Von-Neumann and Morgenstern representation (ie. expected utility representation). If the answer is Yes, provide a Von-Neumann and Morgenstern utility function; otherwise show which Von-Neumann and Morgenstern axiom is violated. (In the figures below, setting p. = 1 - Pr - Py; we describe P as a subset of IR?.) (a) = (plex = 2py + 1} and 12 = {plPr = 4py + 1} (b) h = (plps = 2py + 1} and 12 = {plpr = 2p,} (c) h = (plp, 1/2} (d) h = {ply = (pz)" + 1/2} and 12 = {plpy = (px)}} 3. On a given set of lotteries, find a discontinuous preference relation > that satisfies the independence axiom