Question

​Michelle's Monopoly Mutant Turtle​ (MMMT) has the exclusive right to sell Mutant​ t-shirts in the United States. The demand for these​ t-shirts is Qequals=StartFraction 22 comma 500 Over Upper P squared EndFraction 22,500 P2. The​ firm's short-run cost is SRTCequals=10761076plus+66​Q, and its​ long-run cost is LRTCequals=77Q. What quantity should MMMT sell to maximize profit in the short​ run?

Answer 1

Complete Question:(in order)

Michelle's Monopoly Mutant Turtle (MMMT) has the exclusive right to sell Mutant t-shirts in the United States. The demand for these t-shirts is

$Q = \frac{22,500}{P^2}$

The firm's short-run cost is

SRTC = 1641 + 4Q,

and its long-run cost is

RTC-7Q

What quantity should MMMT sell to maximize profit in the short run?

MMMT should sell 351.56 units. (Enter a numeric response rounded to two decimal places,)

What price should MMMT charge in the short run?

MMMT should charge a price of $ 7.95. Enter a numeric response rounded to two decimal places)

How much profit does it make?

Profit equals $-234.740. (Enter a numeric response rounded to three decimal

Would it be better off shutting down in the short run?

The firm would be better off producing in the short run.

What quantity should MMMT sell in the long run?

MMMT should sell 114.80 units. (Enter a numeric response rounded to two decimal placos)

What price should MMMT charge in the long run?

MMMT should charge a price of $    (Enter a numeric response rounded to two decimal places)

Answer:

From the given parameters

the demand for these t-shirts is

$Q = \frac{22500}{P^2}$

The firms short run cost is SRTC = 1641 + 4Q

Long run cost is  LRTC = 7Q

$=> Q = \frac{22500}{P^2}=> P^2 = \frac{22500}{Q}\\=> P = \sqrt{\frac{22500}{Q}} = \frac{150}{\sqrt{Q}} = 150(Q)^{1/2}$

Thus revenue on the product of price and quantity becomes

$PQ = 150Q^{-1/2}Q = 150Q{1-1/2} = 150Q^{1/2}$

Check the attached files for additional solution