Question

1)A profit maximizing Monopolist has the following total revenue and total cost function

^TR=100q-2q²

TC=50+40q

Where q=output level

You are required to

1.derive the marginal cost

2.derive the marginal revenue

3.calculate the profit maximizing output level

4.determine the profit maximizing selling price.

Answer 1

MC$=$ $\frac{d}{dQ}$ $($ TC$)$ $=$ $\frac{d}{dQ}$ $($ 50$+$ 40q$)$ $=$ 40

MR$=$$\frac{d}{dQ}$$($ TR$)$ $=$ $\frac{d}{dQ}$ $($ 100q$-$ 2q$^2$ $)$ $=$100$-$ 4q

Firm maximize profit when MR$=$MC

100$-$ 4q$=$ 40

q$=$ 15 units

Profit maximizing price:

100$-$ 4q$=$ 100$-$ 4$($ 15$)$ $=$ 40