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Consider a competitive market in which the market demand is given by P = 1000 - Q , where Q is the market quantity. Currently, there are N identical firms and each of them has a cost function c(q) = 25q + 100, where q is an individual firm's supply. Suppose N = 50. Solve the price and quantity sold in the market in equilibrium. Q-200 ; P=800 Q-300; P-700 Q-500; P=500 Q=800; P-2001. Acme, Inc. produces widgets (w) and gadgets (g). Its profit function is given by: IT = 20w-w-+16g -2g a) How many widgets and gadgets should Acme sell to maximize profits? b) Suppose there is a constraint on production such that w + g $ 8. Compute the optimal quantity of widgets and gadgets.Consider a three-person coalitional game in which .((O}) = ((1}) = ({2}) = "({3)) = 0, v({1, 2}) = 6, v({1,3}) = v({2,3}) = 2 and v( {1, 2,3}) = 13. (a) Derive the set of equations/inequalities that characterize the core. (b) What is the maximum payoff that Players 1 and 2 can get in any vector that belongs to the core? (c) Compute the Shapley value. Does it belong to the core?Consider a version of the Solow growth model in which output at time t is determined by the production function Y, = 0.2K, + 0.8L. . The depreciation is given by dK. , where the depreciation rate is d = 0.2. Saving is given by sY, where the saving rate is s = 0.5. Assume that population L t is constant, i.e. does not grow with time. Calculate the steady-state capital per person, ks. Also, calculate the steady-state output per person and consumption per person, y" and c's, respectively