Question 1

Suppose a monopolist knows the own price elasticity of demand for its product is −3 and that its marginal cost of production is constant MC(Q)= 10.To maximize its profit,the monopoly price is:

Accepted Answer

To maximize profit, a monopolist sets price where marginal revenue (MR) equals marginal cost (MC). The formula for MR in terms of elasticity (E) is MR = P(1 + 1/E). Given E = -3 and MC = 10, solve for P: 10 = P(1 + 1/-3), leading to P = $15.

Question 2

Which of the following is a strategy(ies)used by firms in monopolistically competitive industries to convince consumers that their product is better than their rivals' products?

Accepted Answer

Both comparative advertising and niche marketing are commonly used by firms in monopolistically competitive industries to differentiate their products from their competitors. Comparative advertising involves directly comparing the features or benefits of one's own product to those of a competitor's product in advertising. Niche marketing involves targeting a specific segment of the market with unique or specialized products or services.

Question 3

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q)= 100 + 2Q + Q².At the profit-maximizing combination of output and price,consumer surplus is:

Accepted Answer

To find the profit-maximizing output and price, we need to first find the monopolist's marginal revenue (MR) function. We know that the inverse demand function is P = 50 - 2Q, so we can derive the total revenue (TR) function as: TR = P*Q = (50 - 2Q)*Q = 50Q - 2Q^2 Taking the derivative of TR with respect to Q, we get: MR = dTR/dQ = 50 - 4Q Setting MR equal to MC (marginal cost), which is the derivative of total cost with respect to Q, we get: 50 - 4Q = dC(Q)/dQ = 2 + 2² Solving for Q, we get: Q = 9 Substituting this value back into the demand function, we get: P = 50 - 2Q = 32 Therefore, the profit-maximizing output and price are Q = 9 and P = 32. To find consumer surplus, we need to find the area between the demand curve and the price. Integrating the demand function from 0 to 9, we get: ∫0^9 (50 - 2Q) dQ = 405 Integrating the demand function from 0 to 32, we get: ∫0^32 (50 - 2Q) dQ = 512 Therefore, consumer surplus is: 512 - 405 = $107 Since consumer surplus only refers to the benefit consumers receive from purchasing a good, the answer is rounded down to the nearest option, which is option B: $64.

Question 4

SeaSide Industries currently spends 5 percent of its sales on advertising.Suppose that the elasticity of advertising for Seaside is 0.2.Determine the optimal profit margin over price (P − MC)/P.

Accepted Answer

The optimal profit margin over price (P − MC)/P can be calculated as follows:

% Change in Quantity Demanded = Elasticity of Advertising x % Change in Advertising
% Change in Advertising = (New Advertising - Old Advertising)/Old Advertising = (x - 5)/5

As we want to maximize profits, we need to find the advertising spend that maximizes the profit margin. This is achieved when (P - MC)/P is maximized.

Using the formula for price elasticity of demand, we get:

% Change in Quantity Demanded = Elasticity of Advertising x % Change in Advertising
% Change in Quantity Demanded = 0.2 x (x - 5)/5
% Change in Quantity Demanded = (x - 5)/25

Profit margin = (P - MC)/P
Profit margin = (P - (1-0.05)P)/P
Profit margin = 0.05

Therefore, we need to choose the value of x that maximizes the expression (P - MC)/P, which is equal to 0.05.

To maximize profit margin, we want to find the value of x that makes the % change in quantity demanded equal to 0. This is achieved when:

(x - 5)/25 = 0
x - 5 = 0
x = 5

Therefore, Seaside should spend 5% of its sales on advertising to maximize its profit margin.

The optimal profit margin over price is:
(P - MC)/P = 0.05
(1 - MC/P) = 0.05
MC/P = 0.95
(P - MC)/P = (P - 0.95P)/P = 0.05 = 5%

Hence, the correct choice is C.

Question 5

Which of the following is true about where a profit-maximizing monopoly will produce on a linear demand curve when it has positive marginal costs?

Accepted Answer

A profit-maximizing monopoly will produce where marginal revenue (MR) equals marginal cost (MC). On a linear demand curve, this occurs on the elastic portion of the demand curve, where MR is positive.

Question 6

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q)= 100 + 2Q + Q².At the profit-maximizing combination of output and price,deadweight loss is:

Accepted Answer

Deadweight loss in a monopoly can be calculated by finding the area of the triangle formed by the demand curve, the marginal cost curve, and the quantity produced by the monopolist. First, we need to find the monopolist's profit-maximizing quantity and price. The marginal revenue (MR) and marginal cost (MC) are derived from the given functions. The inverse demand function is P = 50 - 2Q, so the total revenue (TR) is P*Q = (50 - 2Q)Q = 50Q - 2Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 50 - 4Q. The total cost (C) is given as C(Q) = 100 + 2Q + Q^2, so the marginal cost (MC) is the derivative of C with respect to Q, which is MC = 2 + 2Q. Setting MR = MC to find the profit-maximizing quantity: 50 - 4Q = 2 + 2Q, solving this gives Q = 12. The price can be found by substituting Q into the demand equation: P = 50 - 2*12 = 26. To find the deadweight loss, we need to find where the MC (which is also the supply curve in a competitive market) intersects the demand curve. Setting P = MC: 50 - 2Q = 2 + 2Q, solving for Q gives Q = 12 (which is the competitive quantity, but we need this to find the intersection point). The deadweight loss is the area of the triangle formed by the demand curve, the MC curve, and the monopolist's quantity. The base of the triangle is the difference between the competitive quantity and the monopolist's quantity (which in this case are the same, so we need to find the height of the triangle, which is the difference in prices). However, the calculation provided directly does not lead to the correct interpretation for deadweight loss calculation. The correct approach involves finding the area of the triangle where the base is the difference between the quantities (which in this case, we need to find the competitive quantity correctly) and the height is the difference in prices. The error in the explanation above is in not correctly identifying the competitive quantity and price, and thus not correctly calculating the deadweight loss. The correct calculation involves finding where the marginal cost equals the average cost for the competitive outcome, which was not accurately pursued. Given the mistake in the process described, the deadweight loss calculation involves finding the area of the triangle where the base is the difference between the monopolist's quantity and the competitive quantity (if correctly calculated) and the height is the difference between the prices at these quantities. Without the correct competitive quantity and price, the direct calculation of deadweight loss as described is not feasible with the given information, leading to an incorrect direct answer. The correct approach to finding the deadweight loss involves more detailed steps in identifying the competitive equilibrium and comparing it to the monopolist's outcome.

Question 7

Suppose that a monopolistically competitive market is at the long-run equilibrium.Based on this information,which of the following conclusions is NOT true?

Accepted Answer

In a monopolistically competitive market at long-run equilibrium, firms face a downward-sloping demand curve, leading to a price (P) that is greater than marginal cost (MC), indicating P > MC. Firms earn zero economic profit in the long run, as new firms enter the market when there are profits, and exit when there are losses, until profits are driven to zero. This is consistent with P = ATC at the quantity produced, but P is greater than the minimum of ATC, indicating some inefficiency and excess capacity. Therefore, unlike in perfect competition, there is a deadweight loss due to the markup over marginal cost, making statement B incorrect.

Question 8

The first-order condition for a monopoly maximizing its profit is:

Accepted Answer

The first-order condition for a monopoly maximizing its profit is given by (dR(Q)/dQ) − (dC(Q)/dQ) = 0, where R(Q) and C(Q) are the revenue and cost functions, respectively. This condition states that the marginal revenue should be equal to the marginal cost for the monopolist to maximize its profit. Therefore, the correct choice is B.

Question 9

Compute the marginal revenue when the price elasticity of demand is −0.25.

Accepted Answer

Marginal revenue (MR) is calculated as MR = P(1 + 1/Ed), where Ed is the price elasticity of demand. With Ed = -0.25, MR = P(1 + 1/(-0.25)) = P(1 - 4) = -3P.

Question 10

Consider firms operating in an industry where the own price elasticity of demand is infinite; that is,E_Q,P = −F1F1F1S1F1F1F10.Use this information to determine the type of industry in which these firms operate and the optimal advertising-to-sales ratio.

Accepted Answer

In a perfectly competitive industry, the own price elasticity of demand is infinite, meaning consumers have perfect substitutes and will switch from one product to another at any price increase. Therefore, firms cannot influence market price and have no incentive to spend on advertising, leading to an optimal advertising-to-sales ratio of 0.

Question 11

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q)= 100 + 2Q + Q².At the profit-maximizing combination of output and price,monopoly profit is:

Accepted Answer

The answer of Consider a monopoly where the inverse demand...

Question 12

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is:

Accepted Answer

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is that the second derivative of the profit function with respect to quantity is negative. This means that the profit function is concave downward, which implies that the marginal cost curve is upward sloping.

Question 13

The first-order conditions for a monopoly to maximize profits are:

Accepted Answer

All the statements represent the same condition for profit maximization in a monopoly, expressed in different mathematical notations. A) Marginal Revenue equals Marginal Cost, B) is another way to state this condition, and C) represents a derivative of profit with respect to quantity equals zero, which is the mathematical condition for maximizing profit.

Question 14

Which of the following features is common to both perfectly competitive markets and monopolistically competitive markets?

Accepted Answer

Both perfectly competitive markets and monopolistically competitive markets have the characteristic of long-run profits being zero. However, A, B, and D are not features common to both markets.

Question 15

The second-order condition for a monopoly maximizing its profit is:

Accepted Answer

The second-order condition for profit maximization in a monopoly involves ensuring that the marginal revenue's rate of change with respect to quantity is less than the marginal cost's rate of change with respect to quantity. This ensures that the profit-maximizing quantity is at a point where profit is maximized, not minimized. The complex expressions in the other options are not standard representations of this condition.

Question 16

The second-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Accepted Answer

The second-order condition for profit maximization requires the second derivative of the profit function (which is revenue minus cost) with respect to quantity to be less than zero. This ensures that the profit function is concave down, indicating a maximum point. Option B correctly represents a condition where the change in revenue minus the change in cost with respect to quantity is less than zero, aligning with the requirement for a maximum profit condition.

Question 17

Consider a monopoly where the inverse demand for its product is given by P = 200 − 5Q.Based on this information,the marginal revenue function is:

Accepted Answer

The formula for marginal revenue is given by:
MR(Q) = ∂TR(Q) / ∂Q
where TR(Q) is the total revenue function.
Total revenue is given by:
TR(Q) = P(Q) × Q
Substituting the given demand function P = 200 − 5Q, we get:
TR(Q) = (200 − 5Q) × Q
TR(Q) = 200Q − 5Q²
Differentiating with respect to Q, we get:
MR(Q) = 200 − 10Q
Therefore, the correct answer is C.

Question 18

Suppose perfectly competitive market conditions are characterized by the following inverse demand and inverse supply functions: P = 100 − 5Q and P = 10 + 5Q.The demand curve facing an individual firm operating in this market is:

Accepted Answer

In a perfectly competitive market, each firm is a price taker, meaning it cannot influence the market price and must accept the prevailing price as given. The demand curve facing an individual firm is therefore perfectly elastic, represented by a horizontal line at the market price.

To find the market price, we can set the inverse demand function equal to the inverse supply function:

100 - 5Q = 10 + 5Q

Solving for Q, we get Q = 9.

Substituting Q back into either equation gives us the market price:

P = 100 - 5(9) = 55

Therefore, the demand curve facing an individual firm is a horizontal line at $55, and the correct answer is C.

Question 19

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Accepted Answer

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is that marginal revenue equals marginal cost, which can be expressed as (dR(Q)/dQ) − (dC(Q)/dQ) = 0. Therefore, the correct answer is C. Choice A is incorrect because it only considers the marginal revenue and marginal cost without taking the differentiation of them into account. Choice B is incorrect because it only considers the price and the cost, without taking their derivatives into account. Choice D is incorrect because it only tells us that the marginal revenue is less than the marginal cost, but it does not provide us with the exact condition for the profit maximization.

Question 20

Which of the following conditions must hold to ensure that profits are,in fact,at a maximum?

Accepted Answer

To ensure that profits are at a maximum, two conditions must hold: 1. Marginal cost (MC) must be equal to marginal revenue (MR), i.e., MC(Q) = MR(Q) 2. The second derivative of profit function with respect to quantity (Q) must be negative, i.e., d^2π/dQ^2 < 0. Option D satisfies both conditions as it states that the first derivative of MC with respect to Q is positive (d(MC(Q))/dQ > 0) and the second derivative of the profit function with respect to Q is negative (d²F1F1F1S1F1F1F10(Q)/dQ² < 0). Hence, option D is the correct choice.

Quiz 8: Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets

Suppose a monopolist knows the own price elasticity of demand for its product is −3 and that its marginal cost of production is constant MC(Q) = 10.To maximize its profit,the monopoly price is:

Which of the following is a strategy(ies) used by firms in monopolistically competitive industries to convince consumers that their product is better than their rivals' products?

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,consumer surplus is:

SeaSide Industries currently spends 5 percent of its sales on advertising.Suppose that the elasticity of advertising for Seaside is 0.2.Determine the optimal profit margin over price (P − MC) /P.

Which of the following is true about where a profit-maximizing monopoly will produce on a linear demand curve when it has positive marginal costs?

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,deadweight loss is:

Suppose that a monopolistically competitive market is at the long-run equilibrium.Based on this information,which of the following conclusions is NOT true?

The first-order condition for a monopoly maximizing its profit is:

Compute the marginal revenue when the price elasticity of demand is −0.25.

Consider firms operating in an industry where the own price elasticity of demand is infinite; that is,E_Q,P = −.Use this information to determine the type of industry in which these firms operate and the optimal advertising-to-sales ratio.

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,monopoly profit is:

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is:

The first-order conditions for a monopoly to maximize profits are:

Which of the following features is common to both perfectly competitive markets and monopolistically competitive markets?

The second-order condition for a monopoly maximizing its profit is:

The second-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Consider a monopoly where the inverse demand for its product is given by P = 200 − 5Q.Based on this information,the marginal revenue function is:

Suppose perfectly competitive market conditions are characterized by the following inverse demand and inverse supply functions: P = 100 − 5Q and P = 10 + 5Q.The demand curve facing an individual firm operating in this market is:

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Which of the following conditions must hold to ensure that profits are,in fact,at a maximum?

Quiz 8: Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets

Suppose a monopolist knows the own price elasticity of demand for its product is −3 and that its marginal cost of production is constant MC(Q) = 10.To maximize its profit,the monopoly price is:

Which of the following is a strategy(ies) used by firms in monopolistically competitive industries to convince consumers that their product is better than their rivals' products?

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q2.At the profit-maximizing combination of output and price,consumer surplus is:

SeaSide Industries currently spends 5 percent of its sales on advertising.Suppose that the elasticity of advertising for Seaside is 0.2.Determine the optimal profit margin over price (P − MC) /P.

Which of the following is true about where a profit-maximizing monopoly will produce on a linear demand curve when it has positive marginal costs?

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q2.At the profit-maximizing combination of output and price,deadweight loss is:

Suppose that a monopolistically competitive market is at the long-run equilibrium.Based on this information,which of the following conclusions is NOT true?

The first-order condition for a monopoly maximizing its profit is:

Compute the marginal revenue when the price elasticity of demand is −0.25.

Consider firms operating in an industry where the own price elasticity of demand is infinite; that is,EQ,P = −.Use this information to determine the type of industry in which these firms operate and the optimal advertising-to-sales ratio.

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q2.At the profit-maximizing combination of output and price,monopoly profit is:

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is:

The first-order conditions for a monopoly to maximize profits are:

Which of the following features is common to both perfectly competitive markets and monopolistically competitive markets?

The second-order condition for a monopoly maximizing its profit is:

The second-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Consider a monopoly where the inverse demand for its product is given by P = 200 − 5Q.Based on this information,the marginal revenue function is:

Suppose perfectly competitive market conditions are characterized by the following inverse demand and inverse supply functions: P = 100 − 5Q and P = 10 + 5Q.The demand curve facing an individual firm operating in this market is:

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

Which of the following conditions must hold to ensure that profits are,in fact,at a maximum?

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,consumer surplus is:

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,deadweight loss is:

Consider firms operating in an industry where the own price elasticity of demand is infinite; that is,E_Q,P = −.Use this information to determine the type of industry in which these firms operate and the optimal advertising-to-sales ratio.

Consider a monopoly where the inverse demand for its product is given by P = 50 − 2Q.Total costs for this monopolist are estimated to be C(Q) = 100 + 2Q + Q².At the profit-maximizing combination of output and price,monopoly profit is: