A video game producer has costs of $ 25,000 per month that are fixed with regard to output. The firm’s marginal cost is $ 5 per unit of output for output between 1 and 15,000 units. Information available from the market research group indicates that 15,000 units could be sold each month in the firm’s primary market if the price was set at $ 6.80 per unit and that 14,000 units could be sold at $ 7 per unit. The market research group also suggests that it is reasonable to assume that price and quantity demanded have a linear relationship in this market not only between those two points, but also well beyond them. 

a. One officer of the firm feels that price should be set at the level that would maximize revenue. At what price would this objective be accomplished? What would price elasticity and marginal revenue be at this price? Is this the price the firm should establish? Why or why not? 

b. Other officers are concerned with profit. What price should be set to maximize profit? What output will prevail in the market at this price? What would price elasticity and marginal revenue be at this price? What is the profit? The firm has the opportunity to sell in a second market that is separated from the first in such a way that buyers in one market cannot resell to buyers in the other market. For the second market, the market research group has estimated the demand relationship to be: 

P₂ = 7 – 0.00001Q₂,

where P₂ is the price in the second market and Q 2 is the quantity of the firm’s product sold in that market each month. 

c. Some officers of the firm believe this second market offers an opportunity for additional profit. They argue that if production is constrained to 15,000 units, the limit within which marginal cost is $ 5, it is worthwhile to sell some of these units in the second market. Should the firm sell any units in this market? Should it sell only units that would not be absorbed in the primary market at the profit- maximizing price? Should it divert some units from the primary to the secondary market? What price would you set in each market? What are the elasticity and marginal revenue in each market? What is the profit if your policy suggestion is followed? How much profit do you attribute to each market? Explain why your suggestion is the best policy. 

d. One of the firm’s production managers has pointed out that 15,000 units of output per month is not the absolute limit on production. The physical limit, she points out, may be closer to 30,000 units. The problem is that for each unit of output above the 15,000-unit level, marginal cost will rise by $ 0.001, so that unit 15,001 will increase total cost by $ 5.001, unit 15,002 will increase it by $ 5.002, and so on. She wonders if the two markets together could not advantageously absorb more than 15,000 units considering this production situation. What total output do you recommend? How much should go into each market? Is it worthwhile to push beyond 15,000 units of output per month? Why or why not?