kindly solve showing your steps

1. (a) Consider an individual making choices over two goods, x and y with initial prices Px = 20 and py = 10, with income I = 1000. If the individual has the utility function u(x, y) = 4x +xy /2; what would the total, income and substitution effects of a price of x decrease to 15? Show your work.1. (20 points) A firm has this production function: 9 = [1/3p1/3 Assume that: w =1 r = 1 K =1 a) (10 points) Suppose this firm is a price-taking firm Show that the firm breaks even (7 = 0) when the price is P = 3 b) (10 points) Suppose this firm is a monopoly The market demand function is P - 90 When operating as a single-price monopoly, show that the firm's maximum profit is n = 286.5 2. (10 points) Turkey is a streaming company which offers TV shows and movies. Engush (upited StateslSuppose we have a constant returns to scale production function with capital, labor, and land, X, which is in fixed supply. The production function is: Y = K"[A(t)L(t)18xx The labor force grows at rate n and labor-augmenting technological progress grows at a fixed rate p. a. What is the sum of the exponents (a + B + A)?. b. Dividing both sides of the production function by L, show that you get the following result: y = k"A x where y, k, and x are measured per worker. c. Show that this implies the following equation (take logs and differentiate):. By = ag + Bp - An where "g" denotes the growth-rate. d. Finally, assume that we are in a steady state where y and k grow at the same rate g*. Find the value for g*. What conditions are necessary for there to be growth in per-capita output in the steady-state? Explain your results intuitivelyLet X be a random variable which has mean & # 0 and variance o?. Let Y be another random variable which has the same mean / and variance o', and suppose the correlation between X and Y is p, where -1