Question

Exercise 10.8

The Poster Bed Company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function for the bed:

P=3,005−10QP=3,005−10Q

The cost analysis department has estimated the total cost function for the poster bed as

TC=Q33−15Q2+5Q+24,000TC=Q33−15Q2+5Q+24,000

Short-run profits are maximized when the level of output is _and the price is $ _.

The total profit at this price-output level is $_.

The point price elasticity of demand at the profit-maximizing level of output is (-4.01, -.02, 0r -.10) .

The level of fixed costs the firm is experiencing on its bed production is $_.

What is the impact of a $5,000 increase in the level of fixed costs on the price charged, output produced, and profit generated?

	Increase	No change	Decrease
Price Charged
Output Produced
Profits Generated

Answer 1

Solution:

For monopolistic competition, short run profit maximization occurs where marginal revenue, MR equals the marginal cost, MC.

Total revenue, TR = price*quantity = P*Q

TR = (3005 - 10*Q)*Q = 3005*Q - 10*Q²

MR = = 3005 - 20*Q

Total cost (as given), TC = (1/3)*Q³ - 15*Q² + 5*Q + 24000

MC = = (3/3)*Q² - 2*15*Q + 5 + 0

MC = Q² - 30*Q + 5

Profit maximization occurs where, MR = MC

3005 - 20*Q = Q² - 30*Q + 5

Q² - 10*Q - 3000 = 0

Factor form: (Q + 50)*(Q - 60) = 0

So, Q = -50 or Q = 60, since quantity cannot be negative, we have profit maximizing level of output as Q* = 60 units

Price, P* = 3005 - 10*60 = $2,405

Total profit at this price and output is:

Profit = 2405*60 - ((1/3)*60³ - 15*60² + 5*60 + 24000)

Profit = 144,300 - (72,000 - 54,000 + 300 + 24000)

Profit = $102,000

Finding the point price elasticity of demand:

P = 3005 - 10*Q

So, modifying this we get, Q = 300.5 - 0.1*P

So, = -0.1

Price elasticity of demand, ed = *(P/Q)

ed = (-0.1)*2405/60 = -4.01 (approximately) . So, correct option is (a).

Fixed costs are the part of total costs which are independent of the quantity, and thus not variable with quantity but fixed. As per this definition, it is easy to see that fixed cost in this case, Fixed costs, FC = $24,000

If the fixed costs increase by $5,000, new FC = 24000 + 5000 = $29,000

Since, fixed cost do not impact the marginal functions in any way, the profit maximizing quantity and price still remain same as before.

However, due to increased fixed costs, profit decrease by that exact same amount of increase in FC. So, new profit = old profit - increase in FC

New profit = 102000 - 5000 = $97,000

So, we can conclude that there is

No change in price charged

No change in output produced

Decrease in the profits generated.