The Madison Corporation, a monopolist, receives a report from a consulting firm concluding that the demand function for its product is Q=78-2P+2Y+0.9A where Q= #of units sold, P=price of products in dollars, Y=per capita income and A = firms advertising expenditure (in thousands of dollars). The firm's average variable cost function is AVC= 42-4Q where AVC is average variable cost (in dollars), and the firm does not incur any fixed costs.
If per capita income is $4,000 and advertising expenditure is $200,000
a. Determine the firm's marginal cost and marginal revenue functions.
b. Find profit maximizing level of output and price for Madison Corp
c. What is the profit at the optimal level f output?