Answer to Question #180207 in Economics of Enterprise for Asmat Ullah Shahid

Question

i.                Following the given equations of costs and its supposed price, find the equilibrium costs and equilibrium quantities

a.    ATC=3Q² +12Q+350,                    P = 60

b.    TC = 300Q² +10Q+120,          P = 40 

Answer 1

(a)a. Given the ATC, calculate TC and the profit equation as below;

$ATC=3Q^{2 }+12Q+350$  

$ATC=\frac{TC}{Q}$

$3Q^{2} +12Q+350=\frac{TC}{Q}$

$TC=3Q^{3 }+12Q^{2}+350Q$

$Profits: π=PQ−TC$

$π=60Q−3Q^{3} −12Q^{2}−350Q$

The firm will maximize profits w.r.t. Q;

At profit maximizing level of Q;

$\frac{∂π}{∂Q}=0$

$60−9Q^{2} −24Q−350=0$

$9Q^{2} +24Q+290=0$

The above quadratic equation in Q has a negave determinant. 

The equation is not satified for any positive 

value of Q.

Q=0

(b)$TC=300Q^{2}+10Q+120$

$\frac{dTC}{dQ}=MC=600Q+10$

$TR=P×Q$

$=40Q$

$\frac{dTC}{dQ}=MR=40$

At equilibrium MR=MC

$40=600Q+10$

$Q=\frac{30}{600}$

$=0.05units$

At equilibrium cost

$TC=300(0.05)^{2}+10(0.05)+120$

$=0.75+0.5+120$

$$121.25$