question on differentiation

Question

Ping's iStove Company produces the very popular iStove in a monopolistic market. Demand for his iStoves, and production costs, are given by the following functions:

Demand: Q = 1200 − 2P ;   Costs: TC = 0.5Q² + 300Q + 18,000. 

a. Specify the marginal revenue (MR) and marginal cost (MC) functions, and find the optimal production level (Q*) using the MR = MC rule.

b. Specify the profit function π(Q) and confirm the optimum production level by checking that the profit function is stationary at Q*. Confirm that profits are increasing when production is less than optimum, and decreasing when production is less than optimum. 

π(Q) = ?

Proof that π is stationary at Q*:

Proof that π is increasing for what domain of Q:   

Proof that π is decreasing for what domain of Q: 

c. Calculate the price consistent with maximum profit, as well as Total Revenue, Total Cost and Profit at this point. 

P* =?

TR* = ?

TC* = ?  

π* =? 

Answer 1