Question

price =10 birr and tc=120+4Q2...then find profit maximizing level of price and quantity

Answer 1

Given:

P=10 birr

TC= 120 + 4Q²

The calculation for profit maximizing level of price and quantity is:

$=(P\times Q)-TC$

$=(10\times Q)-(120+4Q^2)$

$=10Q-120-4Q^2$

Now find derivative to maximize the profit function

$\frac {d}{dQ}(profit)=\frac{d}{dQ}(10Q-120-4Q^2)$

$10-8Q$

Now put derivative equal to zero to find the value of Q

$10-8Q=0$

$8Q=10$

$Q=1.25$

the profit maximizing quantity is 2 and the price is 10 birr