Your company manufactures controllers used in the production of commercial air conditioning units. Your current price is $50 per controller. At that price the total quantity demanded is 4,000 spread over a large number of small customers. Fixed costs are $10,000 per month and marginal costs are $30 for production up to 10,000 units per month. Production cannot be pushed beyond 10,000 units per month. A hurricane has damaged the production facility of a company that produces a low-quality substitute controller. As a result that company has offered you a one-time $35,000 contract for 1,000 controllers to be delivered this month so they can meet the demand of their customers. Within a month the damage to that company's facility will be repaired and they will be back to normal production. Hence this event will not cause your demand curve to shift.
a) Before deciding on the contract you want to analyze your current market. What is the optimal price of your controller if the price elasticity of demand is estimated to be -2 for prices between $45 and $65 per controller?
b) Would you recommend setting your price to that determined in part (a)? Explain why or why not.
c) Would you recommend accepting the offered contract? Explain why or why not.
d) Does your answer to (c) change if your fixed costs are $12,000 per month? Explain why or why not.