Question

1. In a certain city, the movie is monopolistically competitive. In the long run, the demand for movies at given theater is given by the equation:-
P=5.00-0.002 Q where Q is the number of paid admission per month. The average cost function is given by: AC=6-0.004 Q +0.000001 Q2

Required
a. To maximize a profit, what price should the managers of the theatre charge
b. What will be the number of paid admission per month?
c. How much economic profit will the firm earn?
2. A central shop demand for last year was 200 units at the price of $ 8, whereas this years, the quantity demanded is 400 units at price $ 6.
Required
a. What will be the point elasticity of demand for the shop?
b. Interpret the result

Answer 1

1. a. To maximize a profit the managers of the theatre should charge such price, for which P = AC, so:

$5 - 0.002 Q = 6-0.004 Q +0.000001 Q^2,$

$0.000001 Q^2 - 0.002Q + 1 = 0,$

$Q^2 - 2000Q + 1000000 = 0,$

Q = 1,000 units.

P = 5 - 0.002×1,000 = 3.

b. So, the number of paid admission per month is Q = 1,000 units.

c. The economic profit of the firm is zero in the long run, because P = AC.

2. a. The point elasticity of demand for the shop is:

$Ed = \frac{400 - 200} {6 - 8} ×\frac {6 + 8} {400 + 200} = -2.33.$

b. The demand is elastic, because |Ed| > 1.