Dayna’s Doorstops, Inc. (DD) is a monopolist in the doorstop industry. Its cost is C  100  5Q  Q2, and demand is P  55  2Q. a. What price should DD set to maximize profit? What output does the firm produce? How much profit and consumer surplus does DD generate? b. What would output be if DD acted like a perfect competitor and set MC  P? What profit and consumer surplus would then be generated? c. What is the deadweight loss from monopoly power in part a? d. Suppose the government, concerned about the high price of doorstops, sets a maximum price at $27. How does this affect price, quantity, consumer surplus, and DD’s profit? What is the resulting deadweight loss? e. Now suppose the government sets the maximum price at $23. How does this decision affect price, quantity, consumer surplus, DD’s profit, and deadweight loss? f. Finally, consider a maximum price of $12. What will this do to quantity, consumer surplus, profit, and deadweight loss?

Explanation:

Given the following data about Dayna's Doorstep Inc(DD) :

Cost given by; C = 100 - 5Q + Q^2

Demand ; P = 55 - 2Q

A.) Set price to maximize output;

Marginal revenue (MR) = marginal cost (MC)

MR = taking first derivative of total revenue with respect to Q; (55 - 2Q^2)

MC = taking first derivative of total cost with respect to Q; (-5Q + Q^2)

MR = 55 - 4Q ; MC = 2Q - 5

55 - 4Q = 2Q - 5

60 = 6Q ; Q = 10

From

P = 55 - 2Q ;

P = 55 - 2(10) = $35

Output

35(10) - [100-5(10)+10^2]

350 - 150 = $200

Consumer surplus:

0.5Q(55-35)

0.5(10)(20) = $100

B.) Here,

Marginal cost = Price

2Q - 5 = 55 - 2Q

4Q = 60 ; Q = 15

P= 55 - 2(15) = $25

Totally revenue - total cost:

(25)(15) - [100-(5)(15)+15^2] = $125

Consumer surplus(CS) :

0.5Q(55-25) = 0.5(15)(30) = $225

C.) Dead Weight loss between Q=10 and Q=15, which is the area below the demand curve and above the marginal cost curve

=0.5×(35-15) ×(15-10)

=0.5×20×5 = $50

D.) If P=$27

27 = 55 - 2Q

2Q = 55 - 27

Q = 14

CS = 0.5×14×(55 - 27) = $196

DWL = 0.5(1)(4) = $2

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