aanswer the following
(15 points) Suppose the consumer considers goods 1 and 2 to be perfect complements, so that her utility function is u(1, X2) = min {x1, x2}. What is her demand for goods 1 and 2 as a function of income m and prices p1 and p2? Show the derivation, rather than just writing down the demand function if you have it memorized.(20 points) A consumer allocates her income m = 10 between goods 1 and 2, and she considers them to be perfect substitutes: 'u.(a:1, $2) = 3:1 + 3:2. The price of good 2 is $1 per unit, and but the price of good 1 is 2371 per unit. That is, good 1 becomes more expensive if more of good 1 is purchased. (a) Write down an equation expressing the consumer's budget constraint. (b) Draw the budget constraint, labeling the horizontal and vertical intercepts. (0) Draw an indifference curve that passes through the budget constraint. ) ((1 Compute the optimal bundle (1:35:73) demanded by the consumer. (20 points) The market inverse demand curve is P(y) = 10 - 2y, and a monopolist's cost curve is y2 + 2. (a) What output level y maximizes the monopolist's revenue? What output level y maximizes the monopolist's profit? Identify which of the two output levels is lower, and explain why using economic intuition. (b) Suppose a second firm with cost curve y + 2 is considering entering the market. If after entry, the firms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levels y1 and y2 of firms 1 and 2? What would be the equilibrium profits for each firm? Will firm 2 choose to enter the market? (c) Suppose that if firm 2 enters, both firms collude, choosing output levels that maxi- mize total profits and then split the profits equally between them. What would be the profits to each firm? Will firm 2 choose to enter the market in this case?(20 points) The market inverse demand curve is P(y) = 10 - 2y, and a monopolist's cost curve is y2 + 2. (a) What output level y maximizes the monopolist's revenue? What output level y maximizes the monopolist's profit? Identify which of the two output levels is lower, and explain why using economic intuition. (b) Suppose a second firm with cost curve y + 2 is considering entering the market. If after entry, the firms would compete a la Cournot, what would be the Cournot- Nash equilibrium output levels y1 and y2 of firms 1 and 2? What would be the equilibrium profits for each firm? Will firm 2 choose to enter the market? (c) Suppose that if firm 2 enters, both firms collude, choosing output levels that maxi- mize total profits and then split the profits equally between them. What would be the profits to each firm? Will firm 2 choose to enter the market in this case?
