Question

suppose demand and total cost functions for a monopoly firm are given as follow,

demand function- p=800-3Q

Cost function- Tc=60+40Q+Q2

requered;-

1. total revenue function

2.average revenue function

3. average cost function

4.profit maximizing output

5.profit maximizing price

Answer 1

1) Total revenue function.

$=Price(quantity)$

$=(800-3Q)Q$

$=800Q-3Q$²

2) Average revenue function

Average revenue function$=$

$=\frac{\text{Total revenue}}{{Quantity}}$

$=\frac{800Q-3Q^{2}}{Q}$

$\text{Average revenue function}=800-3Q$

3) Average cost function

$\text{Average cost function}=$

$\frac{\text{Total cost function}}{\text{Quantity}}$

$\text{Average cost function}=$

$\frac{60+40Q+Q^2}{Q}$

$\text{Average cost function}$ $=$

$\frac{60}{Q}+40+Q$

4) Profit maximizing output

$\text{Profit maximizing output}=$

$MR=MC$

$MR=\frac{\text{∂TR}}{\text{∂Q}}$

$=800Q-3Q^2$

$=800-6Q$

$MC=\frac{∂TC}{∂Q}$

$=60+40Q+Q^2$

$=40+2Q$

$=MR=MC$

$=800-6Q=40+2Q$

$=800-40=2Q+6Q$

$760=8Q$

$Q=95$

Profit is maximized at $Q=95$

5) Profit maximizing price

$P=800-3Q$

$P=800-3(95)$

$P=800-285$

$P=515$

$\text{Profit maximizing price is}$ $515$