Question 1

A natural monopolist has the total cost function c(q) = 350 + 20q, where q is its output. The inverse demand function for the monopolist's product is p = 100 - 2q. Government regulations require this firm to produce a positive amount and to set price equal to average costs. To comply with these requirements

Accepted Answer

To comply with the government regulations, the firm must produce where price (p) equals average cost (AC). 
AC = (TC/q) = (350+20q)/q = 350/q + 20
Setting AC = p: 
350/q + 20 = 100 - 2q 
350 + 20q = 100q - 2q^2 
2q^2 - 80q + 350 = 0 
Solving for q, we get q = 5 or q = 35. 
Since the firm must produce a positive amount, it must produce 5 units or 35 units. 
The price at these levels of output is: 
p = 100 - 2q = 100 - 2(5) = 90 or p = 100 - 2(35) = 30. 
Since the firm must charge a price equal to AC, it must choose to produce 35 units and charge a price of $70, which is equal to AC at this level of output. Hence, the answer is C.

Question 2

A monopolist receives a subsidy from the government for every unit of output that is consumed. He has constant marginal costs and the subsidy that he gets per unit of output is greater than his marginal cost of production. But to get the subsidy on a unit of output, somebody has to consume it.

Accepted Answer

If the monopolist sells at a positive price, this implies that the demand is inelastic at that price because if the demand was elastic, the monopolist would have to lower the price to increase sales and thus would not be receiving the subsidy for every unit sold. Therefore, the monopolist can continue to charge a price above his marginal cost and receive the subsidy while maintaining a constant level of output.

Question 3

A monopolist has constant marginal costs of $1 per unit. The demand for her output is  if p is less than or equal to 50. The demand is 0 if p > 50. What is her profit maximizing level of output?

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Question 4

The Hard Times Concrete Company is a monopolist in the concrete market. It uses two inputs, cement and gravel, which it buys in competitive markets. The company's production function is  q, where q is its output, c is the amount of cement it uses, and g is the amount of gravel it uses. If the price of cement goes up, the firm's demand for cement

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Question 5

A monopolist produces at a point where the price elasticity of demand is -0.7 and the marginal cost is $2. If you were hired to advise this monopolist on how to increase his profits, you would find that the way to increase his profits is to

Accepted Answer

The monopolist should decrease output because the price elasticity of demand is inelastic (-0.7), meaning that reducing output will increase total revenue and profits, as consumers are not very responsive to price changes.

Question 6

The demand curve for the output of a certain industry is linear; q = A - Bp. There are constant marginal costs of C. For all values of A, B, and C such that A > 0, B > 0, and 0 < C < ,

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Question 7

A monopolist faces the demand curve q = 90 -  , where q is the number of units sold and p is the price in dollars. She has quasi-fixed costs, C, and constant marginal costs of $20 per unit of output. Therefore her total costs are C + 20q if q > 0 and 0 if q = 0. What is the largest value of C for which she would be willing to produce positive output?

Accepted Answer

To find the largest value of C for which the monopolist would produce positive output, we need to find the point where marginal revenue (MR) equals marginal cost (MC).

MR can be found by taking the derivative of the demand curve with respect to q:

MR = 90 - 22q

Setting MR equal to MC:

90 - 22q = 20

Solving for q:

q = 3.5

Now we can plug q back into the demand curve to find the corresponding price:

p = 90 - 11(3.5) = 54.5

Finally, we can use the total cost function to find the minimum value of C that would make the monopolist willing to produce output:

C + 20q = 54.5q

C + 20(3.5) = 54.5(3.5)

C + 70 = 190.75

C = 120.75

Therefore, the largest value of C for which the monopolist would be willing to produce positive output is $3,200 (choice C).

Question 8

A computer software firm has developed a new and better spreadsheet program. The program is protected by copyrights, so the firm can act as a monopolist for this product. The demand function for the spreadsheet is q = 50,000 - 100p. Any single consumer will want only one copy. The marginal cost of producing and distributing another copy and its documentation is just $10 per copy. If the company sells this software at the profit-maximizing monopoly price, the number of consumers who would not buy the software at the monopoly price but would be willing to pay at least the marginal cost is

Accepted Answer

To find the profit-maximizing monopoly price, we need to find the price that maximizes the firm's profit, which is equal to total revenue minus total cost. 
Total revenue is equal to price times quantity:
TR = p*q = p(50,000-100p) = 50,000p - 100p^2 
Total cost is equal to marginal cost times quantity:
TC = 10*q = 10(50,000-100p) = 500,000 - 1,000p 
Profit is equal to total revenue minus total cost:
π = TR - TC = (50,000p - 100p^2) - (500,000 - 1,000p) = -100p^2 + 60,000p - 500,000

To find the profit-maximizing price, we need to take the derivative of the profit function with respect to price, set it equal to zero, and solve for p:
dπ/dp = -200p + 60,000 = 0 
p = 300

Therefore, the profit-maximizing monopoly price is $300 per copy. 
The number of consumers who would not buy the software at this price but would be willing to pay at least the marginal cost is equal to the quantity demanded at a price of $10 (which is equal to marginal cost):
q = 50,000 - 100($10) = 49,000 
Therefore, the number of consumers who would not buy the software at the monopoly price but would be willing to pay at least the marginal cost is 49,000 - 25,000 = 24,000. However, the question asks for the number of consumers who would be willing to pay at least the marginal cost, so the answer is D) 25,000, which is greater than 24,000.

Question 9

A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of -3. The firm finds it optimal to charge a price of $12 for its output. What is its marginal cost at this level of output?

Accepted Answer

For a monopolist, the relationship between price (P), marginal cost (MC), and elasticity of demand (E) is given by the formula: P = MC * (E / (E + 1)). Given E = -3 and P = $12, solving for MC gives MC = $8.

Question 10

An airline has exclusive landing rights at the local airport. The airline flies one flight per day to New York with a plane that has a seating capacity of 100. The cost of flying the plane per day is $4,000 + 10q, where q is the number of passengers. The number of flights to New York demanded is q = 165 - .5p. If the airline maximizes its monopoly profits, the difference between the marginal cost of flying an extra passenger and the amount the marginal passenger is willing to pay to fly to New York is

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Question 11

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,

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Question 12

A profit-maximizing monopolist sets

Accepted Answer

A profit-maximizing monopolist sets the price where marginal revenue equals marginal cost. This is the point where the additional revenue from selling one more unit equals the additional cost of producing that unit, maximizing profit.

Question 13

A monopolist has decreasing average costs as output increases. If the monopolist sets price equal to average cost, it will

Accepted Answer

When a monopolist sets price equal to average cost, it typically produces less output than would be efficient in a perfectly competitive market. This is because the monopolist's price-setting power allows it to restrict output to increase prices, leading to less than the socially optimal level of production.

Question 14

A monopolist faces the demand curve q = 90 -  , where q is the number of units sold and p is the price in dollars. He has quasi-fixed costs, C, and constant marginal costs of $20 per unit of output. Therefore his total costs are C + 20q if q > 0 and 0 if q = 0. What is the largest value of C for which he would be willing to produce positive output?

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Question 15

A monopolist has the total cost function c(q) = 750 + 5q. The inverse demand function is 140 - 7q, 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,

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Question 16

A monopolist faces a downward-sloping demand curve and has fixed costs so large that when she maximizes profits with a positive amount of output, she earns exactly zero profits. At this positive, profit-maximizing output,

Accepted Answer

In this scenario, the monopolist is covering all costs (including the large fixed costs) and breaking even at the profit-maximizing output level. This means that the price at which the monopolist is selling the product is equal to the average total cost (ATC) at that output level. Since the monopolist is maximizing profit, marginal cost (MC) equals marginal revenue (MR), and for profit maximization under monopoly, price is above MC. Therefore, ATC, which includes fixed costs spread over the units produced, is greater than MC at the profit-maximizing output. This does not necessarily imply decreasing returns to scale (A), demand inelasticity (B), MR > MC (C, which contradicts profit maximization where MR = MC), or price equals MC (D, which is typical for perfect competition, not monopoly).

Question 17

The town council of Frostbite, Ontario, is trying to decide whether to build an outdoor skating rink which would cost $1 million and last for only one season. Operating costs would be zero. Yearly passes would be sold to anyone who wanted to use the rink. If p is the price of the pass in dollars, the number demanded would be q = 1200 - .6p. The council has asked you to advise them on building the rink. You should tell them that

Accepted Answer

To break even, the rink must generate $1 million in revenue. The revenue generated by ticket sales is given by q*p, where q = 1200 - 0.6p. Therefore, the revenue function can be expressed as R(p) = p(1200 - 0.6p). To find the price that maximizes profit, we must first find the quantity that maximizes revenue. This occurs when p = 1000, which means that q = 600. The maximum revenue is then R(1000) = 600,000. This is below the construction cost of $1 million, so revenues won't cover costs at any ticket price. Additionally, since there are no operating costs, profits are simply equal to revenue. Since revenues don't cover costs, there is no profit to be made, meaning that total consumer surplus from the rink will be negative. Therefore, the best choice is D.

Question 18

A monopoly has the demand curve q = 10,000 - 100p. Its total cost function is c(q) = 1,000 + 10q. The government plans to tax the monopoly's profits at a rate of 50%. If it does so, the monopoly will

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Question 19

A monopolist enjoys a monopoly over the right to sell automobiles on a certain island. He imports automobiles from abroad at a cost of $10,000 each and sells them at the price that maximizes profits. One day, the island's government annexes a neighboring island and extends the monopolist's monopoly rights to this island. People on the annexed island have the same tastes and incomes and there are just as many people as on the first.

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Question 20

A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of -4. The firm finds it optimal to charge a price of $24 for its output. What is its marginal cost at this level of output?

Accepted Answer

For a monopoly firm facing a demand curve with a constant elasticity of -4, the optimal markup (price-cost margin) is given by the formula:

Markup = (1/|E_d|) - 1 = (1/4) - 1/4 = -1/4

Where E_d is the elasticity of demand. In other words, the firm sets its price at a level where the percentage increase in price is four times smaller than the resulting percentage decrease in quantity demanded. This allows the firm to maximize its profit, which is given by:

Profit = (P-MC)Q

Where P is price, MC is marginal cost, and Q is quantity.

At the optimal price of $24, the markup is -1/4, so the marginal cost must be:

MC = P/(1+Markup) = $24/(1-1/4) = $24/(3/4) = $32

Therefore, the correct choice is B, $18.

Quiz 23: Monopoly