Question 1

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

We can calculate the revenue from selling passes as follows: Total revenue = price per pass * number of passes Total revenue = p(1200 - 0.6p) To make a profit, the total revenue should be greater than the construction cost of $1 million. p(1200 - 0.6p) > $1,000,000 Simplifying the inequality: 0.6p^2 - 1200p + $1,000,000 < 0 Using the quadratic formula: p < ($1200 ± sqrt(1200^2 - 4(0.6)(1,000,000)))/(2(0.6)) p < $800 or p > $1000 Therefore, there is no price at which the ticket revenues still cover costs but total consumer surplus from the rink exceeds costs. Hence, the correct answer is D.

Question 2

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 regulations, the monopolist must charge a price equal to average cost. This means that the price should be equal to total cost divided by output (q).

AC = TC/q = (350 + 20q)/q

Setting this equal to the inverse demand function, we get:

100 - 2q = (350 + 20q)/q

Solving for q, we get:

q = 5 or q = 35

So the firm could produce either 5 units or 35 units to comply with the regulations.

Question 3

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 < A/B,

Accepted Answer

The answer of The demand curve for the output of...

Question 4

A monopolist faces the demand curve q = 90 - p/2, 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 she would be willing to produce positive output, we need to calculate the monopolist's profit at zero output and set it equal to zero. This is because if the profit at zero output is negative, then she would not produce anything, while if the profit at zero output is zero or positive, then she would produce some positive output.

At zero output, the monopolist's total revenue is zero, and her total cost is C. Therefore, her profit is:

π = 0 - C

Setting this equal to zero and solving for C, we get:

0 - C = 0
C = 0

This means that if the quasi-fixed costs are zero, the monopolist would be willing to produce some positive output. However, since the quasi-fixed costs are positive, the monopolist's profit at zero output is negative, and she would not produce anything.

Now, we need to find the largest value of C for which the monopolist's profit is zero or positive. To do this, we need to find the monopolist's output level that maximizes her profit. This is given by:

q* = (90 - C)/(2*20) = (9/4)*(45 - C/9)

Therefore, her profit is:

π = p(q*)*q* - C - 20q*

Substituting the demand function and simplifying, we get:

π = [(45 - C/9)^2]/4 - C(45 - C/9)/2 - (9/2)*(45 - C/9)^2

To find the largest value of C for which the monopolist's profit is zero or positive, we need to solve for C such that:

[(45 - C/9)^2]/4 - C(45 - C/9)/2 - (9/2)*(45 - C/9)^2 = 0

Multiplying both sides by -36 and simplifying, we get:

20C^2 - 12960C + 207360 = 0

Solving for C using the quadratic formula, we get:

C = (12960 ± sqrt(12960^2 - 4*20*207360))/(2*20) ≈ 3200 or ≈ 648

Since the monopolist's quasi-fixed costs cannot be negative, the largest value of C for which she would be willing to produce positive output is:

C = $3,200

Therefore, the answer is (C).

Question 5

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

Accepted Answer

The monopoly maximizes profit where marginal revenue equals marginal cost. A profit tax does not affect marginal cost or marginal revenue, so the monopoly's price and quantity remain unchanged.

Question 6

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 7

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 = c^1/2g^1/2q, 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

Accepted Answer

The correct answer is C because the demand for cement and gravel are both inputs in the production of concrete. If the price of cement goes up, the firm may use less cement and more gravel, or vice versa, depending on the demand function for concrete.

Question 8

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 9

A monopolist faces the demand curve q = 90 - p/2, 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?

Accepted Answer

Explanation:The monopolist will produce positive output if and only if p > 20. The revenue function is R = pq = 90p - p^2/2. The profit function is pi = R - C - 20q = 90p - p^2/2 - C - 20(90 - p/2) = 50p - p^2/2 - C. The profit-maximizing quantity is q = 45 - p/4. Substituting this into the profit function, we get pi = 50(45 - p/4) - (45 - p/4)^2/2 - C = 2250 - 25p + p^2/8 - C. The profit-maximizing price is p = 40. Substituting this into the profit function, we get pi = 2250 - 25(40) + 40^2/8 - C = 1600 - C. The monopolist will produce positive output if and only if 1600 - C > 0, which implies that C < 1600. The largest value of C for which the monopolist would be willing to produce positive output is therefore $1,600.

Question 10

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,

Accepted Answer

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.

Question 11

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

Accepted Answer

The answer of An airline has exclusive landing rights at...

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 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.

Accepted Answer

The monopolist can keep the price constant and double sales because the annexed island has the same demand conditions, effectively doubling the market size.

Question 14

A monopolist has constant marginal costs of $1 per unit.The demand for her output is 1,000/p if p is less than or equal to 50.The demand is 0 if p > 50.What is her profit maximizing level of output?

Accepted Answer

To maximize profits, the monopolist should produce where marginal revenue (MR) equals marginal cost (MC).

- When p is less than or equal to 50, the demand function is 1000/p. Therefore, the revenue function is R = pq = 1000q/p. 
- The marginal revenue function is the derivative of the revenue function with respect to q: MR = dR/dq = 1000/p. 
- Since the marginal cost is constant at $1 per unit, the monopolist should produce where MR = MC = 1: 
1000/p = 1 
p = 1000

Since p cannot be greater than 50, the monopolist should produce at the highest possible price, which is $50. Therefore, the profit maximizing level of output is: 
q = 1000/50 = 20.

Question 15

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

The answer of A computer software firm has developed a...

Question 16

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

We know that the demand curve has a constant elasticity, so we can use the formula:

E = (% change in quantity demanded) / (% change in price) = (dQ/Q) / (dP/P)

where E is the elasticity, Q is the quantity demanded, and P is the price.

We also know that the firm is maximizing profit, which means that it is producing at the point where marginal revenue (MR) equals marginal cost (MC). Therefore, we can use the following formula for Marginal Revenue:

MR = P (1 + 1/E)

At the profit-maximizing level of output, we have P = $24, and E = F1F1F1S1F1F1F104.

Solving for MR, we get:

MR = $24 (1 + 1/ F1F1F1S1F1F1F104)

Next, we need to find MC at this level of output. We know that MR = MC, so:

$24 (1 + 1/ F1F1F1S1F1F1F104) = MC

Solving for MC, we get:

MC = $18

Therefore, the answer is B) $18.

Question 17

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

The marginal cost can be found using the formula for the optimal pricing rule for a monopolist, which is P = MC * (E / (E - 1)), where P is the price, MC is the marginal cost, and E is the price elasticity of demand. Given the constant elasticity of -3, we substitute P = $12 and E = -3 into the formula and solve for MC, which gives us MC = $8.

Question 18

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, he can only do so if the demand is inelastic at that price, otherwise consumers will not buy his product. As the monopolist has constant marginal costs, any subsidy he receives will increase his profit for each unit he produces and sells. Therefore, even if he sells at a lower price due to the subsidy, he would still make a profit as long as the demand remains inelastic at that price.

Question 19

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 20

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,

Accepted Answer

The answer of A monopolist has the total cost function...

Quiz 23: Monopoly-Part A