2) Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b>0. a. Suppose the market is served by two firms acting in a cartel. Calculate the profit- maximizing: i. Price ii. iii. Quantity Profit

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2) Assume firms' marginal and average costs are constant and equal to c and that
inverse market demand is given by P = a bQ where a, b>0.
a. Suppose the market is served by two firms acting in a cartel. Calculate the profit-
maximizing:
i. Price
ii.
iii. Profit
b. Suppose now the market is served by 2 firms (one leader, and one follower) that
choose quantities for their identical products. Calculate:
i. The Nash equilibrium quantities for the Stackelberg duopolists
ii.
Quantity
iv. Firm profit
Market output
Market price
c. Suppose now the market is served by 2 firms that choose quantities for their
identical products simultaneously. Calculate:
iv.
i. The Nash equilibrium prices for Cournot duopolists
ii.
Firm output
Market output
Firm profit
ii.
iii.
iv.
d. Suppose now the market is served by k firms that choose quantities for their
identical products simultaneously. Calculate:
i. The Nash equilibrium quantities for the Cournot firms as functions of k.
Market output and price as a function of k
Firm profit as a function of k
Using your answers in i, ii, iii and iv, describe what happen to firm output,
market output, market price and firm profit as the number of firms
increases.
Transcribed Image Text:2) Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a bQ where a, b>0. a. Suppose the market is served by two firms acting in a cartel. Calculate the profit- maximizing: i. Price ii. iii. Profit b. Suppose now the market is served by 2 firms (one leader, and one follower) that choose quantities for their identical products. Calculate: i. The Nash equilibrium quantities for the Stackelberg duopolists ii. Quantity iv. Firm profit Market output Market price c. Suppose now the market is served by 2 firms that choose quantities for their identical products simultaneously. Calculate: iv. i. The Nash equilibrium prices for Cournot duopolists ii. Firm output Market output Firm profit ii. iii. iv. d. Suppose now the market is served by k firms that choose quantities for their identical products simultaneously. Calculate: i. The Nash equilibrium quantities for the Cournot firms as functions of k. Market output and price as a function of k Firm profit as a function of k Using your answers in i, ii, iii and iv, describe what happen to firm output, market output, market price and firm profit as the number of firms increases.
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