Economics 11

Question 1 (Market Demand) Suppose there are three consumers for good X. For each of the following consumers, find the demand curve (x expressed as a function of px. This is same as saying find the Marshallian demand and plug in I). You can use the Cobb-Douglas formula. (a) Consumer 1 with the utility function U(x, y) = x0.5y0.5 and income I = 100. (b) Consumer 2 with the utility function U(x, y) = x0.3y07 and income / = 200. (c) Consumer 3 with the utility function U(x, y) = x0.60.4 and income / = 150. Now, find the market (aggregate) demand for good X by summing up the x's you found. (d) Find the market demand curve (QD as a function of Px).Question 3 (Equilibrium) 200 Suppose the market demand is QB = T and the market supply is Q; = 2N P, where N is the number of rms in the market. Suppose N = 25. (a) What are the short-run equilibrium price and the equilibrium quantity? (b) What is the output level for each rm? (0) What is the prot for each rm? ((1) Repeat part (a) through (c) for N = 4-00. (e) Repeat part (a) through (c) for N = 100. (i) What is the long-run equilibrium price and the equilibrium quantity? (g) How many rms are there in the longrun equilibrium