A publisher faces the following demand schedule for the next...

A publisher faces the following demand schedule for the next novel from one of its popular authors: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?

A publisher faces the following demand schedule for the next novel from one of its popular
authors: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?

Key Concepts

Economic Efficiency

Economic efficiency is achieved when goods are produced at a level where the marginal benefit to consumers equals the marginal cost of production—typically when price equals marginal cost. A firm or policy that focuses on maximizing efficiency rather than profit aims to eliminate deadweight loss and ensure the optimal distribution of resources, even if it means lower profits or negative profit.

Marginal Cost and the MR=MC Condition

Marginal cost represents the cost of producing one additional unit, and firms rely on the MR=MC condition to determine the profit?maximizing quantity. The point where the marginal revenue curve intersects the marginal cost curve is critical because it signals that any further increase in production would add more cost than revenue, thereby reducing profit.

Deadweight Loss

Deadweight loss measures the loss in total surplus that occurs when market output is not at the socially optimal level, typically because the quantity produced is less than or greater than the level where demand equals marginal cost. Graphically, it is represented by the area between the demand and the marginal cost curves that is not captured by the existing market equilibrium, reflecting inefficiencies in allocation.

Total Revenue and Total Cost Analysis

This concept deals with calculating total revenue by multiplying the price by the quantity sold and computing total costs by summing fixed costs and variable (marginal) costs. Analyzing these totals at each quantity level allows firms to determine the profit, which is the difference between total revenue and total costs. Understanding these calculations is crucial for making informed production and pricing decisions.

Profit Maximization

Profit maximization involves choosing the level of output or price that yields the highest difference between total revenues and total costs. For monopolistic publishers or firms with market power, this decision is based on analyzing both fixed and variable costs, as well as how price changes with quantity sold on the demand schedule. The key condition used is setting marginal revenue equal to marginal cost, which indicates that producing one more unit would not add to profit.

Marginal Revenue Analysis

Marginal revenue is the additional revenue generated from selling one more unit of output. It is calculated as the change in total revenue divided by the change in quantity sold. In markets where the demand curve is downward sloping, the marginal revenue is typically less than the price because a price reduction is necessary to sell additional units, affecting all units sold.

Transcript

00:01 Okay, guys, this is chapter 15 problem 1.

00:05 In this problem, we are given this table up here in the corner.

00:11 It's the price and demand schedule for a publisher in his book.

00:16 We're saying we're given that the author is paid $2 million to write the book, and then the marginal cost.

00:23 The publishing the book is constant at $10 per book.

00:26 In this first part, we're asked to compute the total revenue, total cost, and profit at each quantity and then determine how much the publisher would produce.

00:37 And so for each quantity, you know, for zero, the quantity of zero, the total revenue, they're not selling anything, so here's revenue, here's cost, and here's profit.

00:54 So revenue is going to be zero.

00:55 The cost is $2 million because they still have to pay the author even if they don't sell anything and so the profit is going to be minus two million then when they sell 100 ,000 you're going to get a hundred thousand times uh 90 dollars per book that's nine million the cost is going to be one million plus the two one million for actually making the books plus two million uh to pay to the author and that's going to be three million you get a profit of six million so then for 200 ,000 uh you're going to get you know 80 times 200 ,000 six million the cost then two million dollars for the books plus two million dollars to be author is four million and your profit's going to be 12 million uh so honestly you should continue to go through all of this uh it's a very simple calculation i'm not going to do it all i'm just going to finish with at 500 ,000, which is going to end up being our profit maximizing amount.

02:05 Our revenue is going to be 25 million, and it's going to cost 7 million for a profit of 18 million.

02:15 So the publisher is going to produce 500 ,000.

02:22 Computing the marginal revenue in part b, and we're given here that this formula marginal revenue equals the change, in total revenue divided by the change in quantity and so when you go from zero to 100 ,000 you're going to have a profit change in profit of 9 million divided by a change in quantity of 100 ,000 is going to give you marginal revenue of 90 when you go from 100 ,000 to 200 ,000 you get a change in total revenue of 7 million 7 million.

03:03 The change in quantity is still 100 ,000 and you're going to get 70 and you can start to see a pattern here at 300 ,000.

03:12 It's 5 million divided by 100 ,000 equals 50.

03:18 And again, you should continue doing this, but you see it's a pretty clear pattern.

03:22 It decreases by $20 each time.

03:25 And then marginal revenue is always less than the price.

03:32 And this implies that the publisher has monopoly power.

03:45 For the third part, we're then asked to graph marginal revenue, marginal cost, and demand.

03:55 So again, our trustee supply and demand graph.

03:57 We have quantity demanded, we have price.

04:02 Price up here at $100.

04:05 We sell nothing...