Question

 Given P = 24 – 0.1Q, where Q = q1+q2 and q1 = q2, TC1 = 0.1q1 2 , TC2 = 0.05q2 2 , a) Determine the output and price of low-costfirm b) Calculate the profit of the low-cost firm c) What isthe profit maximizing price level the high firm would like to charge but that doesn’t realize in the market? d) Compare the profits of the price taker at its own profit maximizing output and low-cost firm’s output e) Show the results a to d graphically 

Answer 1

profit and cost is maximised when MR=MC

p=24-0.1q

TR=PQ

=(24-.1Q)q

TR=24Q-0.1$q^2$

MR=$\frac{d(TR)}{dQ}$ =24-0.2q

TC=TC1+TC2

TC=0.1q₁$^2$ +0.05q₂$^2$

MC₁=$\frac{d(TC1)}{dQ1}$ =0.2q₁

MC2=$\frac{d(T2)}{d2}$ =0.1q₂

mr₁=mc₁

24-0.2q₁=0.2q₁

24=0.4q₁

q₁=60

mr₂=mc₂

24-0.2q₂=0.1q₂

24=0.3q₂

q₂=80

remember Q=q₁+q₂

Q=60+80

Q=140

P=24-0.1Q

P=24-(0.1$\times140)$

p=$10

b) profit=TR-TC

TR=QP

=140$\times$ 10

=$1400

Tc₁=0.1$\times$60$^2$

=0.1$\times$ 3600

=$360

tc₂=0.05$\times$ 80$^2$

=0.05$\times$ 6400

=$320

TC=360+320

=680

TC-TR

=1400-680

Profit=$720

c)

price=profit divide by quantity

$\frac{720}{140}$ =$5.14