How does marginal revenue relate to the price for a perfectly competitive firm? Describe how this relationship captures the firm’s incentive (or lack of incentive) to produce additional units of output.
How does marginal revenue relate to the price for a firm with market power? Describe how this relationship captures the firm’s incentive (or lack of incentive) to produce additional units of output.
Why do we draw the marginal revenue curve below the demand curve?
Is marginal revenue positive or negative? Or zero? Explain.
Suppose a firm faces an inverse demand curve \(P = 100 - 2Q_D\text{.}\)
Use the twice-as-steep rule to derive the equation for the marginal revenue function.
Graph demand and marginal revenue on the same graph.
If the firm wants to produce 15 units of output, what is the highest price the firm can charge? Use demand, and draw this point on your graph.
If the firm wants to produce 15 units of output, how much additional revenue does the last unit generate for the firm? Use marginal revenue, and draw this point on your graph.
What is price elasticity of demand when the firm produces 15 units of output?
Subsection7.6.2Profit maximization with market power: Monopoly
For a monopolist, is marginal revenue equal to marginal cost for each unit of output produced?
How does marginal analysis support the monopolist’s profit-maximization condition? Explain in words.
How does marginal analysis support the monopolist’s profit-maximization condition? Draw a graph of marginal revenue and marginal cost, indicating the range of \(q\) when output is too low, the range of \(q\) when output is too high, and the optimal quantity of output \(q^*\text{.}\)
Consider a monopoly where demand is \(P = 80 - q\text{;}\) marginal revenue is \(MR = 80 - 2q\text{;}\) total cost is \(TC = 3q^2\text{;}\) and marginal cost is \(MC = 6q\text{.}\)
Find the optimal quantity of output for the monopolist, \(q^*_M\text{.}\)
Find the optimal price the monopolist will charge, \(P^*_M\text{.}\)
Calculate the amount of profit the monopolist makes at \(q^*_M\text{.}\)
Calculate the firm’s optimal price markup, denoted by \(\frac{P}{MC}\text{.}\)
Calculate price elasticity of demand at this point \((P^*_M, q^*_M)\text{.}\)
Consider a monopoly where demand is \(P = 100 - q\text{;}\) marginal revenue is \(MR = 100 - 2q\text{;}\) total cost is \(TC = q^2 + 20\text{;}\) and marginal cost is \(MC = 2q\text{.}\)
Find the optimal quantity of output for the monopolist, \(q^*_M\text{.}\)
Find the optimal price the monopolist will charge, \(P^*_M\text{.}\)
Calculate the amount of profit the monopolist makes at \(q^*_M\text{.}\)
Calculate the firm’s optimal price markup, denoted by \(\frac{P}{MC}\text{.}\)
Calculate price elasticity of demand at this point \((P^*_M, q^*_M)\text{.}\)
Subsection7.6.3Welfare analysis
Compared to perfect competition, how do price and quantity differ in a monopoly? Why does this happen?
Compared to perfect competition, how does consumer surplus differ in a monopoly? Why does this happen?
Does deadweight loss exist in a monopoly?
Consider a monopoly where demand is \(P = 80 - q\text{;}\) marginal revenue is \(MR = 80 - 2q\text{;}\) total cost is \(TC = 3q^2\text{;}\) and marginal cost is \(MC = 6q\text{.}\)
Find the optimal quantity of output for the monopolist, \(q^*_M\text{.}\)
Find the optimal price the monopolist will charge, \(P^*_M\text{.}\)
Graph the monopoly outcome in a carefully-labeled graph, including demand, \(MR\text{,}\)\(MC\text{,}\)\(q^*_M\text{,}\) and \(P^*_M\text{.}\)
Calculate consumer surplus and indicate it on your graph.
Calculate producer surplus and indicate it on your graph.
Consider a monopoly where demand is \(P = 100 - q\text{;}\) marginal revenue is \(MR = 100 - 2q\text{;}\) total cost is \(TC = q^2 + 20\text{;}\) and marginal cost is \(MC = 2q\text{.}\)
Find the optimal quantity of output for the monopolist, \(q^*_M\) and the optimal price the monopolist will charge, \(P^*_M\text{.}\)
Graph the monopoly outcome in a carefully-labeled graph, including demand, \(MR\text{,}\)\(MC\text{,}\)\(q^*_M\text{,}\) and \(P^*_M\text{.}\)
Calculate consumer surplus and producer surplus under the monopoly, and indicate each on your graph.
Find the competitive equilibrium outcome, \(q^*_{PC}\) and \(P^*_{PC}\text{.}\)
Calculate consumer surplus and producer surplus at the competitive equilibrium outcome. How do they compare with your answers from c.?
MonacoNet is an internet service provider (ISP) in a small town. As the only provider in town, the firm has market power. Demand for internet service is given by the inverse demand function \(P = 300 - 0.5Q_D\text{.}\) This gives their marginal revenue function as \(MR = 300 - Q_D\text{.}\) The marginal cost for MonacoNet is given by \(MC = cQ\text{,}\) where \(c > 0\text{.}\) MonacoNet considers how many connections it is optimal for them to offer.
Here, the firm’s marginal revenue is not equal to the price. Is it higher or lower than price? Explain why in words.
Does MonacoNet experience diminishing marginal product of labor? How can you tell?
Calculate the quantity of output (\(q^*\)) which maximizes the firm’s profit. Calculate the price (\(P^*\)) the firm will charge. Both will depend on the parameter \(c\text{.}\)
Draw demand, marginal revenue, and marginal cost in a carefully-labeled graph when \(c = 4\text{.}\)
Suppose that due to a technological development, MonacoNet’s marginal cost is cut to \(c = 2\text{.}\) Calculate the firm’s new optimal quantity, and the new price they will charge. Draw the shift on a graph.
Does the decrease in cost benefit MonacoNet? Does the decrease in cost benefit consumers? Use the values above and additional calculations to support your answers.
Subsection7.6.4Measures of market power
How does a firm’s price compare to its marginal cost when the firm has market power?
Does the price elasticity of demand for a firm’s product impact its ability to mark up is price? If so, how?
How can we express a firm’s price markup\(\frac{P}{MC}\) in terms of the price elasticity of demand, \(\epsilon_D\text{,}\) for the firm’s product?
How can we express a firm’s Lerner index\(\ell\) in terms of the price elasticity of demand, \(\epsilon_D\text{,}\) for the firm’s product?
Calculate the price markup for a firm whose product has a price elasticity of demand is \(\epsilon_D = -1.5\text{.}\)
Calculate the price markup for a firm whose product has a price elasticity of demand is \(\epsilon_D = -3\text{.}\)
If a firm can mark up its price 5 times its marginal cost, what is the price elasticity of demand for the firm’s product?
Consider a firm whose product has a price elasticity of demand of \(\epsilon_D = -2\text{.}\)
Calculate the firm’s price markup, \(\frac{P}{MC}\text{.}\)
If the firm’s marginal cost is $20 when it is maximizing its profit, how high of a price will it charge?
Calculate the firm’s Lerner index, \(\ell\text{.}\)
If the firm’s marginal cost is $20 when it is maximizing its profit, what percentage of its price will be markup?
Consider a firm whose competes in a perfectly competitive market, and therefore has no market power.
What is the shape of the firm’s residual demand curve? Draw it out.
What does this mean for the price elasticity of demand for the firm’s product? Give the \(\epsilon_D\) value.
Calculate the firm’s price markup, \(\frac{P}{MC}\text{,}\) using the \(\epsilon_D\) value.
Explain in words why this value makes sense given the market structure.
Calculate the firm’s Lerner index, \(\ell\text{,}\) using the \(\epsilon_D\) value
Explain in words why this value makes sense given the market structure.
Subsection7.6.5Monopolistic competition
Give the assumptions of the monopolistic competition market structure.
Describe a real-world market which fits the description of monopolistic competition. Explain in words why the market fits the assumptions so well.
From where does a monopolistically competitive firm’s market power come? How is this different from market power in a monopoly?
How does a monopolistically competitive firm behave in the short run?
One a single graph, draw a monopolistically competitive firm’s demand, marginal revenue, marginal cost, and average total cost. Indicate the firm’s optimal choice of output, \(q^*\text{,}\) and the price it charges ,\(p^*\text{.}\) Indicate the shaded areas representing its total revenue, total cost, and profit.
What happens in monopolistic competition in the long run?
Can a monopolistically competitive firm maintain its market power in the long run? Explain why or why not.
