Hi. Kindly solve these problem

Consider the following utility function of 2 goods, x and y: U[x,y]|= [{x 101'2 + {yli'i ]; x,yal] The prices of good x and y is 10 and 20 respectively. The income is denoted by m. a] Draw the indifference curves for the utility function and use arrows to explain in which direction utility increases or decreases. [3 points] b} Find the consumption bundle or bundles that maximizes utility for the consumer. [4 poirrts] c] Find the Engel curve for both goods. [4 points] Suppose the utility function changes and now it is: mosh-101*: + {yrlure ; was: dj Draw the indifference curves for the utility function and use arrows to explain in which direction utility increases or decreases. [3 points] e] Find the consumption bundle or bundles that maximizes utility for the consumer. [4 points] f} Find the Engel curve for both goods. [4 points] 4. (5 points) Consider the utility function u(x, y) = 10 In(x) + y. (a) Let px = 10 denote the price of x, let py = 1 denote the price of y and let / = 100 denote the income. Find the utility maximizing bundle. (b) If px = 5 and the price of y and income are as in part (a), then find the expenditure minimizing bundle to get to the utility level from part (a). (c) Fix the income at / = 100 and p. = 2. Is there any price range for y where only good x will be purchased, that is, the optimal bundle will have y = 0?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.A perfectly competitive firm has a Cobb-Douglas production function f (X1, X2) = X,X2- Suppose that input prices are W, = 1 and W2 = 1. The firm wants to find the cheapest way of producing y = 32. a. Suppose that in the short run the quantity of input factor 2 is fixed at X2 = 8. Solve the firm's short-run cost minimization problem to derive the optimal input quantity xi . b. Derive the corresponding costs Cs of producing y = 32 in the short run. c. Now consider the long run, in which both input factors are variable. Set up the Lagrangian function for this firm's long-run cost minimization problem. d. Derive the first-order conditions of the above long-run cost minimization problem. e. Solve the above first-order conditions to derive the optimal input quantities x, and X2. f. Derive the corresponding costs c' of producing y = 32 in the long run.Acme widget company has the plant capacity to produce 100 widgets or 100 zercs. Acme's current production mix is 55 widgets and 45 zercs. What is the total cost of producing 55 widgets? A. 45 zercs C B. 55 zercs C C. I zerc D. There is not enough information to tell. What would be the marginal cost of producing the fifty sixth widget? (Curl)