# Consider the market for vegan soup where two firms

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Consider the market for vegan soup, where two firms, Kibble and Flesh Not, are in Stackelberg competition. Flesh Not observes Kibble's output level before choosing its desired output level. The market inverse demand curve for vegan soup is P = 18 Q, where Q measures cups of soup produced by Kibble and Flesh Not, q K and q F , and P i s the price per cup. Kibble and Flesh Not produce soup at a constant marginal cost of \$2. a. Derive Flesh Not's reaction function. b. Derive Kibble's marginal revenue function. c. How much output does Kibble produce? d. How much output does Flesh Not produce? e. What is the market price of vegan soup?
and 2 . ) K K
71 6 The inverse market demand curve for American alligators is P = 4,000 2 Q, where Q is the quantity of alligators and P is the market price. American alligators can be produced at a constant marginal cost of \$1,000, and all American alligators are identical. a. Suppose the American alligator market is served by two firms that form a c split the market output. What is the market output and price level? b. Suppose the American alligator market is served by two firms that are enga competition. What is the market output and price level? c. Suppose the American alligator market is served by two firms that are enga competition. The inverse market demand curve P = 4,000 2( q 1 + q 2 ), whe output, Q, is the sum of each firm's output, q 1 + q 2. What is the market outp d. Suppose the American alligator market is served by two firms that are enga Stackelberg competition. The inverse market demand curve P = 4,000 2( market output, Q, is the sum of each firm's output, q 1 + q 2. What is the mark price level? q Q 2 . 2 2 .
4,000 2 q 1 4 q 2 =1,000 Solve for q 2 , Firm 2's reaction function: q 2 = 750 0.5 q 1 . Use the two-reaction function to solve for each firm's output. Plug Firm 2's reaction function into Firm 1's reaction function: q 1 = 750 0.5(750 0.5 q 1 ) q 1 = 500 q 2 = 500 Q = 500 + 500 = 1,000 P = 4,000 2(1,000) = \$2,000 d. Assume that Firm 1 is the Stackelberg leader (i.e., the firm that sets the output level first), although the answers to this question would not change if Firm 2 were the Stackelberg leader. Plug Firm 2's reaction function into the market inverse demand curve: