Answer to Question #285962 in Macroeconomics for Aster

Question

Suppose a firm has its TR and TC functions given as follows:

        TR =300 Q -3Q² and TC =500 +50 Q +2Q²

         A. State the profit function of the firm

         B. State the marginal profit function.

         B .Find the level of Q that maximizes total profit.

         D .State the marginal revenue function  

         E .State the marginal cost function.

Answer 1

Solution:

A.). The profit function = TR – TC = (300Q – 3Q²) – (500 + 50Q + 2Q²)

= 300Q – 50Q – 3Q² – 2Q² – 500 = 250Q – Q² – 500

Profit function = 250Q – Q² – 500

 

B.). Marginal Profit function = $\frac{\partial \pi } {\partial Q} =$ 250 – 2Q

 

C.). Profit maximization is where MR = MC:

MR = $\frac{\partial TR} {\partial Q} =$ 300 – 6Q

MC = $\frac{\partial TC} {\partial Q} =$ 50 + 4Q

 

300 – 6Q = 50 + 4Q

300 – 50 = 4Q + 6Q

250 = 10Q

Q = 25

Profit maximizing output = 25 units

 

D.). Marginal Revenue function: MR = $\frac{\partial TR} {\partial Q} =$ 300 - 6Q

 

E.). Marginal cost function: MC = $\frac{\partial TC} {\partial Q} =$ 50 + 4Q