Reference no: EM132871963

Question - 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.

Firm A's Marginal Cost $5.00 and Capacity is 30

Firm B's Marginal Cost $7.10 and Capacity is 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.

(a) Find equilibrium prices for this one-time pricing game.

(b) Suppose that before the pricing game starts, Firm A can build a production plant that would have full capacity of 100 units.

Ignoring the cost of building, how much profit would Firm A earn if it expanded? Firm A would now earn profits of ______________.