Question

Given the following inverse demand and cost function, answer the questions below:
$P(Q)=60-\frac{Q}{2}$
$C(Q)=20Q$


a) Suppose barriers to entry exist such that only one firm serves the market with no threat of entry. What will be the monopoly price, outcome, and profit?
b) Suppose instead that perfect competition exists in this market. What will be the competitive price, market quantity Q, and competitive firm profit?
c) Suppose two firms serve the market with no threat of entry. If the two firms compete in quantities, what will be the Cournot price, quantity for each firm, and market quantity, and profit for each firm?
d) Suppose the same two firms decide to compete on prices, still with no threat of entry. What will be the Bertrand price, quantity for each firm, market quantity, and profit for each firm? e) Suppose that we know have a two period game, in which a leading firm determines its quantity based on how it expects the follower firm to respond. Find the Stackelberg price, quantity for each firm, market quantity, and profit for each firm.
f) Graph the price and market quantity pairs on a graph of demand, identifying the monopoly, Cournot, Stackelberg, Bertrand, and perfectly competitive outcomes.

Answer 1

a) me. 2 = 20 P=60-0h TR-600 - 0² Me-R 600 Profit is man when MR-me 6ord=2000-40) P=60-40 - 40 T = (4020) (46)-800 6) 26 Pesses competition Pane 60-8= 20 = 80 Jall-ro T = 600,- 0 - 0 0 - 2000 h = 60- 01-02-20 =0 - 0, 40-0 2009, Due to synnericity 02 - 800 solong 0,402 O2 = 80 - [sool 160-80t0202 80+02_Yel2 O 2 = 80 = 1.-26.66 Pruci = 60-2180 o - 33.333 d) T1 = T12 = 13.33 126:66) = 355.3778 In case of Berband compektion P = P2 = 20 & total = 80 Toi-02-40 Profit of each fin ao