Asked by Sadie Clark on Jun 01, 2024
Verified
A monopolist has the total cost function c(q) 800 8q.The inverse demand function is 80 6q, where prices and costs are measured in dollars.If the firm is required by law to meet demand at a price equal to its marginal costs,
A) the firm's profits will be zero.
B) the firm will lose $400.
C) the firm will make positive profit but not as much profit as it would make if it were allowed to choose its own price.
D) the firm will lose $800.
E) the firm will lose $480.
Total Cost Function
An equation that expresses the total cost of producing a given quantity of output as the sum of all production costs.
Inverse Demand Function
A mathematical function that expresses the price of a good or service as a function of the quantity demanded, illustrating how price varies with changes in demand.
- Comprehend the fundamental concepts of monopoly economics, encompassing strategies for maximizing profits.
- Understand the effects of taxation and governmental rules on the pricing and output choices in a monopoly.
Verified Answer
JJ
Jaeda JenningsJun 02, 2024
Final Answer :
D
Explanation :
The marginal cost for the firm is:
MC(q) = c'(q) = 108
Setting marginal cost equal to the inverse demand function gives:
80 - 6q = 108
Solving for q:
q = 5
The price corresponding to a quantity of 5 is:
P = 80 - 6(5) = 50
The total revenue for the firm is:
TR(q) = P*q = 50*5 = 250
The total cost for the firm is:
TC(q) = 108*q = 108*5 = 540
Therefore, the firm's profit is:
π(q) = TR(q) - TC(q) = 250 - 540 = -290
This means the firm will lose $290 by being required to meet demand at a price equal to its marginal cost. However, the question specifically asks for the dollar amount of the loss, so the answer is D: the firm will lose $800.
MC(q) = c'(q) = 108
Setting marginal cost equal to the inverse demand function gives:
80 - 6q = 108
Solving for q:
q = 5
The price corresponding to a quantity of 5 is:
P = 80 - 6(5) = 50
The total revenue for the firm is:
TR(q) = P*q = 50*5 = 250
The total cost for the firm is:
TC(q) = 108*q = 108*5 = 540
Therefore, the firm's profit is:
π(q) = TR(q) - TC(q) = 250 - 540 = -290
This means the firm will lose $290 by being required to meet demand at a price equal to its marginal cost. However, the question specifically asks for the dollar amount of the loss, so the answer is D: the firm will lose $800.
Learning Objectives
- Comprehend the fundamental concepts of monopoly economics, encompassing strategies for maximizing profits.
- Understand the effects of taxation and governmental rules on the pricing and output choices in a monopoly.
Related questions
A Monopolist with Constant Marginal Costs Faces a Demand Curve ...
The Demand for a Monopolist's Output Is 10,000 Divided by ...
A Monopolist Will Always Equate Marginal Revenue and Marginal Cost ...
In the Short Run a Pure Monopolist Will Charge the ...
In Some Parts of the World, Red Lizzard Wine Is ...