Question

The XYZ corporation, a monopolist, receives a report from a consulting firm concluding that the demand function for its product is:

Q = 80 – 1.5P + 2.3M + 0.75A

Where Q is the number of units sold, P the price of its product, M is buyers’ per capita income, and A is the firm’s advertising expenditure. The total cost function is:

C(Q) =50,000 + 42Q – 8Q2 + 1.5Q3

Buyer’s per capita income is estimated to be $10,000 and the firm spends $200,000 on advertising.

a. How much output should the firm produce to maximize profit (minimize loss)?

b. What price should be charged for the output?

c. How much profit (loss) does the firm make?

Answer 1

Demand function is Q = 80-1.5p+2.3M+ 0.75A

=80 -1.5p + 23,000 + 150,000

P = (173080 - Q)/1.5

Total revenue = PQ =

Marginal Revenue =

Total cost function is c(Q) = 50,000 + 42Q -9Q2 +1.5Q3

Marginal Cost = = 42Q

For profit maximization output , MR = MC

= 2837

a) SO , profit maximizing output = 2837.

b) TO determine price , put Q obtained in demand equation.

P =

= 113,495

c)Profit or loss = P*Q - C(Q)

=113,495 * 2837 - (50,000 + 42 *2837 -8Q2 + 1.5Q3)

I hope this helps .I fyou have any queries , put in the comments.I will modify/edit my answer according to your requirments.

Have a nice day :)