Question

1.) Mustapha maintains a monopoly in the holographic TV market because of its patent but it...

1.) Mustapha maintains a monopoly in the holographic TV market because of its patent but it is about to expire. The market demand and Mustapha’s production cost are given by: P = 100 − 0.5? and ?? = 100 + 0.5Q2 The monopoly profit is.

a. $3,750.00

b. $2,400.00

c. $3,000.00

d. $2,500.00

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Answer #1

Answer

Option b) $2400

Reason:

The monopolist’s demand curve

P = 100 - 0.5Q

generates the total revenue equation. ( TR = P*Q )

TR= 100Q - 0.5Q2

Also total cost equation is

TC = 100 + 0.5Q2

Given these equations, the profit-maximizing quantity of output is determined through the following steps:

Determine marginal revenue by taking the derivative of total revenue with respect to quantity.

dTR/ dQ = 100 -Q

Determine marginal cost by taking the derivative of total cost with respect to quantity.

dTC/ dQ = Q

Set marginal revenue equal to marginal cost and solve for q.

100 - Q = Q

Thus, Q = 50

Substituting 50 for Q in the demand equation enables you to determine price.

P = 100 - 0.5*50 = $75

Thus, Monopoly profit = TR -TC

=  100Q - 0.5Q2 - 100 - 0.5Q2

= 100Q - 100 - Q2

= 5000 - 100 - 2500

= $2400

   

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