Hi. Kindly solve these

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?Assume that the production function of your country at period t is given by Y(t) = A(t)K(t)"L(t)1-", where a = 0.3, Y is output, K is capital, L is labor, and A is the technological level of the country. Assume for now that A(t) = 1 in any period. Also assume that the depreciation rate of capital is o =0.01. 1. Write the production function in per capita terms. 2. Write the main equation of the Solow model (in per capita terms) using this production function.Problem 3: The market for product Q has many identical firms, each having the short-run total cost function: STC(q) = 400+5q+q?, where q is the firm's annual output. We also know that the market demand curve for Q is given by: Q =262.5 - 0.5P, where P is the market price. Each firm is currently earning zero economic profit. (a) Calculate numeric values for: E the market price, (ii) each firm's output, the number of firms in the market. (b) State the market level supply curve. (c) Draw the market and firm demand/supply graphs and show your results from parts (a) and (b).Question 1: Consider an industry with only two firms. The industry inverse demand curve is given by: P = 120 - Q where P is the market price and Q is total industry output. Let each firm have identical marginal cost of $20 and produce identical products. In addition, there are no fixed costs of production. Suppose the firms engage in Cournot strategic competition. Find the Cournot equi- librium price P and industry output Q. Determine the profits for each firm in the Cournot equilibrium