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Chapter 15: Problem 1

A publisher faces the following demand schedule for the next novel from one of its popular authors: $$\begin{array}{cc} \text { Price } & \text { Quantity Demanded } \\ \hline \$ 100 & 0 \text { novels } \\ 90 & 100,000 \\ 80 & 200,000 \\ 70 & 300,000 \\ 60 & 400,000 \\ 50 & 500,000 \\ 40 & 600,000 \\ 30 & 700,000 \\ 20 & 800,000 \\ 10 & 900,000 \\ 0 & 1,000,000 \end{array}$$ The author is paid \(\$ 2\) million to write the book, and the marginal cost of publishing the book is a constant \$10 per book. a. Compute total revenue, total cost, and profit at each quantity. What quantity would a profitmaximizing publisher choose? What price would it charge? b. Compute marginal revenue. (Recall that \(M R=\Delta T R / \Delta Q .\) ) How does marginal revenue compare to the price? Explain. c. Graph the marginal-revenue, marginal-cost, and demand curves. At what quantity do the marginal-revenue and marginal-cost curves cross? What does this signify? d. In your graph, shade in the deadweight loss. Explain in words what this means. e. If the author were paid \(\$ 3\) million instead of \(\$ 2\) million to write the book, how would this affect the publisher's decision regarding what price to charge? Explain. f. Suppose the publisher was not profit-maximizing but was instead concerned with maximizing economic efficiency. What price would it charge for the book? How much profit would it make at this price?

Short Answer

Expert verified
To find the profit-maximizing quantity and price: compute total revenue, total cost, and profit at each quantity, and choose the quantity with the highest profit. Marginal revenue is less than the price beyond the first unit. Marginal-revenue and marginal-cost curves cross at the quantity where profit is maximized. Deadweight loss is the potential gains that did not occur due to market inefficiency. The price would remain unchanged if the author's payment increased to \)3 million, as this is a fixed cost. For maximizing economic efficiency, the price should be set equal to MC, leading to zero profit.

Step by step solution

01

- Determine Total Revenue

Total revenue (TR) is calculated by multiplying the price (P) by the quantity demanded (Q). Calculate TR for each price level given in the demand schedule.
02

- Determine Total Cost

Total cost (TC) includes the fixed cost of paying the author (\(2 million) and the marginal cost (MC) of producing each book (\)10 per book). Calculate TC for each quantity level as TC = Fixed Cost + (MC * Q).
03

- Calculate Profit

Profit is calculated by subtracting total cost from total revenue (Profit = TR - TC). Calculate profit for each quantity level.
04

- Determine Profit-Maximizing Quantity

Identify the quantity at which profit is the highest. This will be the profit-maximizing quantity.
05

- Determine Corresponding Price

Find the price that corresponds to the profit-maximizing quantity determined in Step 4 from the demand schedule.
06

- Compute Marginal Revenue (MR)

Calculate the change in total revenue (Delta TR) divided by the change in quantity (Delta Q) to find the marginal revenue at each level of output. Remember that MR = Delta TR / Delta Q.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Total Revenue Calculation
Understanding how to calculate total revenue (TR) is essential for any business, including the publishing industry described in our scenario. Total revenue is the amount of money a company receives from sales of its products or services. It is calculated by multiplying the price at which the product is sold by the quantity sold:
\(TR = Price \times Quantity\).
The demand schedule provided gives different price points and the corresponding quantity demanded. By applying the total revenue formula at each price level, we get a clear picture of the revenue generated at that specific price point. This computation is critical as it lays the groundwork for determining profitability and making strategic business decisions.
Profit Maximization
Profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. There are several ways to approach this, but one of the most common is finding a balance between the cost to produce and the revenues received.
For the given publisher, profit maximization involves assessing the total revenue against the total costs, which include both fixed costs (like the author's fee) and variable costs (such as the constant printing cost per book). The goal here is to find the quantity at which the difference between TR and TC is the greatest. This involves performing calculations at each quantity level to determine where profit peaks. Choosing this optimal quantity and corresponding price ensures that the publisher is operating in a manner that maximizes financial returns.
Marginal Cost
Marginal cost (MC) is a fundamental principle in economics that represents the cost of producing an additional unit of a good or service. It is crucial to understand because it helps firms decide whether or not it's beneficial to increase production. The MC remains constant at $10 per book in the publisher's case.
MC can also be compared with marginal revenue to determine the best level of output. In general, firms increase output until the point where MC equals marginal revenue (MR), which is also the point of profit maximization. However, if MC were to change—due to increased costs for materials or labor, for example—that could shift the profit-maximizing quantity.
Marginal Revenue
Marginal revenue (MR) is the additional revenue that is gained by selling one more unit of an item. It's an essential concept because it helps a company make decisions about how much of a product to supply. For a perfect competition scenario, marginal revenue is equal to the price of the product. However, for firms with more control over their prices (like our publisher), the MR might not align with the price.
Computing MR involves finding the change in total revenue from selling one more unit (\(MR = \frac{\Delta TR}{\Delta Q}\)). In the case of our publisher, they would calculate MR at each level of output and look for the point where MR equals MC. This intersection informs the publisher about the profit-maximizing level of output, assuming that increasing output does not significantly change MC.
Economic Efficiency
Economic efficiency occurs when a company produces a good or service at the lowest possible cost and wastes the least amount of resources. It's all about optimizing the production and distribution of goods to achieve the best possible outcome for both producers and consumers. For our publisher, maximizing economic efficiency might not always align with profit maximization. If the publisher were concerned with economic efficiency rather than maximizing profit, they would set a price and production level where the price equals the MC of production.
At this point, known as the allocative efficiency point, the value consumers place on the last unit they are willing to buy (reflected by the price they pay) is equal to the cost of making that unit. While this approach may not yield the highest possible profits, it ensures resources are not misspent or overproduced, minimizing wasteful expenditures and optimizing overall satisfaction in society.

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Most popular questions from this chapter

A company is considering building a bridge across a river. The bridge would cost \(\$ 2\) million to build and nothing to maintain. The following table shows the company's anticipated demand over the lifetime of the bridge: $$\begin{array}{cc} \text { Price per Crossing } & \begin{array}{c} \text { Number of Crossings, } \\ \text { in Thousands } \end{array} \\ \hline \$ 8 & 0 \\ \hline 7 & 100 \\ 6 & 200 \\ 5 & 300 \\ 4 & 400 \\ 3 & 500 \\ 2 & 600 \\ 1 & 700 \\ 0 & 800 \end{array}$$ a. If the company were to build the bridge, what would be its profit- maximizing price? Would that level of output be efficient? Why or why not? b. If the company is interested in maximizing profit, should it build the bridge? What would be its profit or loss? c. If the government were to build the bridge, what price should it charge? d. Should the government build the bridge? Explain.

A small town is served by many competing supermarkets, which have the same constant marginal costs. a. Using a diagram of the market for groceries, show the consumer surplus, producer surplus, and total surplus. b. Now suppose that the independent supermarkets combine into one chain. Using a new diagram, show the new consumer surplus, producer surplus, and total surplus. Relative to the competitive market, what is the transfer from consumers to producers? What is the deadweight loss?

Henry Potter owns the only well in town that produces clean drinking water. He faces the following demand, marginal-revenue, and marginal-cost curves: $$Demand: P=70-Q \ Marginal Revenue: M R=70-2 Q\ Marginal cost: M C=10+Q$$ a. Graph these three curves. Assuming that Mr. Potter maximizes profit, what quantity does he produce? What price does he charge? Show these results on your graph. b. Mayor George Bailey, concerned about water consumers, is considering a price ceiling 10 percent below the monopoly price derived in part (a). What quantity would be demanded at this new price? Would the profit-maximizing Mr. Potter produce that amount? Explain. (Hint: Think about marginal cost.) c. George's Uncle Billy says that a price ceiling is a bad idea because price ceilings cause shortages. Is he right in this case? What size shortage would the price ceiling create? Explain. d. George's friend Clarence, who is even more concerned about consumers, suggests a price ceiling 50 percent below the monopoly price. What quantity would be demanded at this price? How much would Mr. Potter produce? In this case, is Uncle Billy right? What size shortage would the price ceiling create?

Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new DVD:$$\begin{aligned} &\text {Demand:} P=1,000-10 Q\\\ &\text {Total Revenue:}T R=1,000 Q-10 Q^{2}\\\ &\text {Marginal Revenue:}M R=1,000-20 Q\\\ &\text {Marginal cost:}M C=100+10 Q \end{aligned}$$ where \(Q\) indicates the number of copies sold and \(P\) is the price in Ectenian dollars. a. Find the price and quantity that maximize the company's profit. b. Find the price and quantity that would maximize social welfare. c. Calculate the deadweight loss from monopoly. d. Suppose, in addition to the costs above, the director of the film has to be paid. The company is considering four options: i. a flat fee of 2,000 Ectenian dollars. ii. 50 percent of the profits. iii. 150 Ectenian dollars per unit sold. iv. 50 percent of the revenue. For each option, calculate the profit-maximizing price and quantity. Which, if any, of these compensation schemes would alter the deadweight loss from monopoly? Explain.

Many schemes for price discrimination involve some cost. For example, discount coupons take up the time and resources of both the buyer and the seller. This question considers the implications of costly price discrimination. To keep things simple, let's assume that our monopolist's production costs are simply proportional to output so that average total cost and marginal cost are constant and equal to each other. a. Draw the cost, demand, and marginal-revenue curves for the monopolist. Show the price the monopolist would charge without price discrimination. b. In your diagram, mark the area equal to the monopolist's profit and call it \(X\). Mark the area equal to consumer surplus and call it \(Y\). Mark the area equal to the deadweight loss and call it \(z\). c. Now suppose that the monopolist can perfectly price discriminate. What is the monopolist's profit? (Give your answer in terms of \(X, Y,\) and \(Z .\) ) d. What is the change in the monopolist's profit from price discrimination? What is the change in total surplus from price discrimination? Which change is larger? Explain. (Give your answer in terms of \(x, Y,\) and \(z .\) ) e. Now suppose that there is some cost associated with price discrimination. To model this cost, let's assume that the monopolist has to pay a fixed cost \(C\) to price discriminate. How would a monopolist make the decision whether to pay this fixed cost? (Give your answer in terms of \(X\), \(Y, Z, \text { and } C .)\) f. How would a benevolent social planner, who cares about total surplus, decide whether the monopolist should price discriminate? (Give your answer in terms of \(X, Y, Z,\) and \(C .\) ) g. Compare your answers to parts (e) and (f). How does the monopolist's incentive to price discriminate differ from the social planner's? Is it possible that the monopolist will price discriminate even though doing so is not socially desirable?
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