Calculate the Monopolistically Competitive Equilibrium? Part 2?

Question

C. If not, what output, price, and economic profits will occur in equilibrium? Assume equilibrium occurs through a parallel leftward shift in the demand curve. (Hint: the slope of the average cost curve = -$150,000/Q2.)

D. Calculate Silas’s new equilibrium demand curve.

Answer 1

C:

ATC=TC/Q

ATC=400+150'000/Q

P=4'500-Q

We should shift demand curve until P-ATC=0 or maximization/minimization condition first order derivative (ATC-P)'=0

(4'500-Q-400-150'000/Q)'=0

150'000/Q^2-1=0

150'000/Q^2=1

150'000=Q^2

Q=387.3

ATC(387.3)=787.3

TC(387.3)=304'913.33

Demand should touch ATC at point Q=387.3

ATC at this point will be ATC=787.3 and at this point also P should be equal P=787.3

Shift of demand will be: P=4'500-(Q-X)

Since P=787.3 and Q=387.3 then

787.3=4'500-(387.3-X)

X=-3325.4 (it will shift left for 3325.4)

New equilibrium Q=387.3 P=787.3

TR(387.3)=787.3*387.3= 304'919.33

TC(387.3)=150'000+400*387.3= 304919.33

Profit=TR-TC=0

D:

Final demand will be:

P=4'500-3325.4-Q

P=1174.6-Q