Question

A publisher faces the following demand schedule for the nextnovel by one of its popular authors. The author is paid $2million to write the book, and the MC ofpublishing the book is aconstant $10 per book.

P	Q	TR	MR	TC	Profit	ATC
100	0	0
90	100,000	9,000,000	90
80	200,000	16,000,000	35
70	300,000	21,000,000	17
60	400,000	24,000,000	8
50	500,000	25,000,000	2
40	600,000	24,000,000	-2
30	700,000	21,000,000	-4
20	800,000	16,000,000	-6
10	900,000	9,000,000	-8
0	1,000,000	0	-9

1-What quantity thisprofit-maximizing publisher choose and at what price?

2-How does MR Compares to price?Explain.

3-Graph the D, MR, MC andATC.

4-Show the deadweight loss on thegraph and explain what it means.

5-If the author were paid $3instead of $2 million to write the book, how would this affect thepublisher’s decision regarding theprice? Explain.

6-Suppose the publisher is not aprofit-maximizing but were concerned with maximizing economicefficiency. What price would thepublisher charge for thebook? How much profit would the publisher make at this price?

Answer 1

A monopolist will use some of the same logic as a perfectly competitive firm in making pricing decisions. Specifically, the monopolist behaves like a PC firm in

    1) Ignoring Fixed Costs in deciding how much to produce (at least in the short run). Note that the amount the author is paid does NOT vary with quantity.

    2) Producing more units as long as the change in revenues from making one more unit (aka the marginal Revenue) exceeds the difference in total costs from making one more unit (aka the Marginal Cost). 

In perfect competition, the price is fixed, so the marginal Revenue is just the price. If I make one more book and sell it for, say, $20, then my total revenues go up by$20.

However, for a monopolist, the price is NOT fixed. If the monopolist wants to sell more units, she has to lower the cost. And that decrease in prices will reduce the revenues from all the other teams she was already selling.

For example: suppose you can sell two books for $10 each, with total revenues of $20. Now you think about pricing instead of sell3 books. You'll have to lower the price to $8 to induce that3rd buyer to buy. When you drop your price and sell the3rd book, you get $8 in revenues from the new sale--but you LOSE $2in Revenue from the 1st sale and $2 in Revenue from the 2ndsale. Your payments go up from $20 (2*$10) to $24(3*$8) for an MR of $4. Your Marginal Revenue is LESS than the price because of this lowered-prices-on-earlier-sales effect.

To solve a monopoly problem, you need to locate the point where MR = MC (or, for "lumpy" problems like this, the last moment before MR<MC). That is, locate the point where the extra revenues from a new sale are still more than the additional costs of the recent sale. That point tells you the quantity.

The price is whatever price the consumers will pay for the quantity you just determined. If you're graphing, you find the amount where the MR curve and MC curve cross, then go up to the Demand Curve at that same quantity to get the price.

In this problem, the MC is 10. Looking at the MR table, MR for 70 is 17 and for 60 is only 8, which is the first point where MR is lower than 10. So if you drop the price to 60, the extra Revenue you get doesn't make up for the additional costs you have to pay. The price is still way above the MC, so on paper, it looks like new books are "paying for themselves," but discounting the books any farther to get more sales will cause you to lose too much Revenue on prior sales.

I'll leave you on your own for the graphing.

Deadweight Loss is the Loss in total surplus because an inefficient quantity has been produced, so to find DWL, you first have to identify the efficient amount.

The efficient quantity (in the absence of an externality) is where MC = D. The efficient amount will be based on the demand at a price equal to the MC or a price equal to10. The monopolist will choose to sell only 300,000 units, but the benevolent social planner (if you're using that metaphor)would decide to produce 900,000 units. The consumer and producer surplus lost on those "missing" 600,000 units is the DWL. This is the region between the MC and the demand curve from Q(monopolist) to Q(efficient point).