Kindly solve these questions.

Part III - Worked Problem (40 points) Assume that the market demand for oil in a country can be described by: Q =80 - 2P Also assume that oil production is controlled by the government and the cost of production can be described by: MC = 10 +Q a) What would oil price and quantity be in the country if competitive prices are charged to consumers? What is the net welfare to society at this price and quantity? b) Suppose the oil market develops into a monopoly in that country. What is the new price and quantity in the monopoly market? What is the net welfare to society at the monopoly price and quantity? c) Now, the country is allowing international trade and some competitive international producers (i.e. competitive fringe) enter the market. The marginal cost of the competitive fringe is: MC = 20 + Qc The domestic oil producer now has to face some competition, but remains a dominant firm. Applying the dominant firm model to the situation with a new competitive fringe, what would be the domestic oil producer's level of output, the price charged by the domestic producer, and what would be the competitive international producers' level of output as a group? Why is the domestic producer the dominant firm?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?A firm uses inputs of labor, L, and capital, K, to produce its output, Q, according to the production function Q=f(X,L)-9LUSKVS. The firm is a price-taker in the input markets. Labor is paid an hourly wage of w = 12, and the price of capital is r =6. The firm sells its output at a price of p = 4 per unit. 1) Maximize the profit function to determine the optimum level of each input the firm should use. 2) Check second-order sufficient condition. Show your calculations.A firm has technology represented by the following production function: f ( L, K) = L^1/3 K ^2/3 It would like to produce 122 units. It operates in competitive input markets where the price of labor is $6 and the price of capital is $9. What amount of labor does the firm use when it is producing its desired level of output in the least costly way?Suppose X has mean 2 and variance 9. Suppose Y has mean 5 and variance 25. Also, assume that the Cov(X, Y) = -6. a) What is the correlation coefficient between X and Y? (b) What is the variance of X + Y? (e) What is the variance of 11X - 8Y? Suppose X has mean 2 and variance 9. Suppose Y has mean 5 and variance 25. Also, assume that the Cov(X, Y ) = -6. (a What is the correlation coefficient between X and Y? (b) What is the variance of X + Y? (c What is the vanance of 11X - 8Y