Question

(This question is a variation on the pricing dilemma game from class.) Two firms, A and B, sell widgets to a market of 100 buyers. The firms' widgets are undifferentiated, and the firms know each others' costs and capacities. Furthermore the firms are playing a one-time pricing game; widgets are obsolete after this one selling opportunity. Each buyer is interested in purchasing a single widget, and has an RP of $10.

Firm A has lower costs than Firm B, but also has lower capacity. Specifically, their (constant) marginal costs and capacities are as follows.

	Marginal Cost	Capacity
Firm A:	5	30
Firm B:	7.1	100

Finally, assume that each firm can only post prices in whole dollar amounts. (This question is motivated by firms selling through coin-operated vending machines. It is too costly to stock such machines with pennies, so sellers must set prices in fixed increments of larger denomination coins.) Throughout this entire problem, firms may only choose prices of $1.00, $2.00, $3.00, ..., up to $10.00. Firms may NOT use prices such as $1.50, $2.99, $3.83, etc.

(2a.) Find equilibrium prices for this one-time pricing game. (As usual: all buyers go to the firm with the lowest price. However if Firm A's price is no higher than Firm B's price, Firm A serves only 30 buyers, and the rest go to Firm B. Your answer should be a pair of prices, one for each firm.) (6 points)

(2b.) Suppose that before the pricing game starts, Firm A can build a production plant that would have full capacity of 100 units. (Marginal costs would remain the same, and Firm B would see Firm A's new capacity. Then firms would simultaneously set some equilibrium prices.)

Ignoring the cost of building, how much profit would Firm A earn if it expanded?  Firm A would now earn profits of ______________. (You must show your calculations for credit. The same assumptions apply as the previous part, except now the firms split the market 50/50 if they price equally.) (4 points)

Firm A:

Firm B:

Marginal Cost

$5.00

$7.10

Capacity

30

100

Answer 1

2a) Firm A will set the price at $8 (that is closest to Firm B's MC) and it knows that Firm B cannot go lower than $7.10 but since they can quote price only in round numbers,they will quote the next integer;8.

and firm B sets price at $8(closest to its MC,hence it cannot go lower than $7.10. This way Firm A serves 30 buyers, and the rest go to Firm B. Firm A's profit=30 x (8-5)=$90

2b) If Firm A expands,it can serve 50 buyers. Hence it earns net profit of 50 x (8-5)= $150