Question

In: Economics

The monopolist: "You Can't Handle the Ruth" sells baseball cards. It has a fixed cost of...

The monopolist: "You Can't Handle the Ruth" sells baseball cards. It has a fixed cost of $5000 in rent, and a variable cost of

2Q. Q is t he number of baseball cars which are sold. The firm faces a market demand curve of P=200-Q.  

What is the firms profits maximizing equilibrium?

How much profits is the firm making?  

Should it stay open or shut down?  

Solutions

Expert Solution

Demand Function

P = 200 - Q

Profit is maximized where marginal revenue and marginal cost both are equal

Marginal revenue can be calculated from the demand curve by doubling the coefficient of Q

MR = 200 - 2Q

Total Cost Function

TC = 5000 + 2Q

Marginal cost can be calculated from the total cost function by differentiation.

MC = dTC / dQ

MC = 2

Equating MR and MC

200 - 2Q = 2

Q = 99

Hence the equilibrium quantity is 99 units

To find the equilibrium price we will use this quantity in demand function.

P = 200 - Q

P = 200 - (99)

P = 101

Profit = Total Revenue - Total Cost

Total Revenue = Price x Quantity

Total Revenue = 101 x 99

Total Revenue = 9999

Total Cost = 5000 + 2Q

Total Cost = 5000 + 2(99)

Total Cost = 5198

Profit = Total Revenue - Total Cost

Profit = 9999 - 5198

Profit = 4801

A firm should shut down when it is not able to cover its average variable cost from price so at 99 units price is $101 and

AVC = VC / Q

AVC = 2Q / Q

AVC = 2(99) / 99

AVC = 2

As price is greater than AVC hence the should continue to produce and should not shut down.


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