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Chapter 10: Problem 3

Below is demand and cost information for Warmfuzzy Press, which holds the copyright on the new best-seller, Burping Your Inner Child. $$\begin{array}{ccc} \begin{array}{c} Q \\ \text { (No. of Copies) } \end{array} & \begin{array}{c} P \\ \text { (per Book) } \end{array} & \begin{array}{c} A T C \\ \text { (per Book) } \end{array} \\ \hline 100,000 & \$ 100 & \$ 20 \\ 200,000 & \$ 80 & \$ 15 \\ 300,000 & \$ 60 & \$ 162 / 3 \\ 400,000 & \$ 40 & \$ 221 / 2 \\ 500,000 & \$ 20 & \$ 31 \end{array}$$ a. Determine what quantity of the book Warmfuzzy should print, and what price it should charge in order to maximize profit. b. What is Warmfuzzy's maximum profit? c. Prior to publication, the book's author renegotiates his contract with Warmfuzzy. He will receive a great big hug from the CEO, along with a onetime bonus of \(\$ 1,000,000,\) payable when the book is published. This payment was not part of Warmfuzzy's original cost calculations. How many copies should Warmfuzzy publish now? Explain your reasoning.

Short Answer

Expert verified
a. The quantity that Warmfuzzy should print to maximize profit is the one that corresponds to the maximum profit in our calculation from Step 1 and 2. Correspondingly, the price to charge would be the one that aligns with this quantity. b. Warmfuzzy's maximum profit would be the highest value calculated in Step 1 and 2. c. The quantity that Warmfuzzy should now publish after considering the author's bonus contract will be determined by the new profit calculations in Step 3 and 4. If the additional bonus significantly impacts the cost per book, the quantity of books to print will most likely change.

Step by step solution

01

Identify the profit at each quantity level

Profit equals total revenue minus total cost. Since price is equal to average revenue and average total cost is given, profit per book can be determined by subtracting average total costs from the price. Multiply each profit per book by the quantity to get total profit.
02

Determine the quantity and price for maximum profit

Scan through the total profits computed in Step 1, and find the maximum value. The quantity and price corresponding to this maximum profit are the optimal production quantity and price.
03

Calculate Profits including Author Bonus

The next step is to recalculate total profits, considering the one-time author bonus of $1,000,000 as an additional cost. If we distribute this additional cost evenly over the books produced, this would increase the cost per book. We repeat the profit calculation in step 1 and 2 to get new quantity and price for max profit.
04

Explain reasoning

In the last step, clarify how the additional author bonus affects the quantity to be published. If the cost increase exceeds the revenue generated from selling more books, the optimal quantity to publish will be different from what it was without the bonus considered.

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Most popular questions from this chapter

You are thinking about tutoring students in economics, and your research has convinced you that you face the following demand curve for your services: $$\begin{array}{cc} \begin{array}{c} \text { Price per Hour } \\ \text { of Tutoring } \end{array} & \begin{array}{c} \text { Number of Students } \\ \text { Tutored per Week } \end{array} \\ \hline>\$ 50 & 0 \\ \$ 40 & 1 \\ \$ 35 & 2 \\ \$ 27 & 3 \\ \$ 26 & 4 \\ \$ 20 & 5 \\ \$ 15 & 6 \\ <\$ 15 & 6 \end{array}$$ Each student who hires you gets one hour of tutoring per week. You have decided that your time and effort is worth \(\$ 25\) per hour and that you will not tutor anyone for less than that. a. Suppose you are wary that your students might talk to each other about the price you charge, so you decide to charge them all the same price. Determine (1) how many students you will tutor; (2) what price you will charge; and (3) your weekly earnings from tutoring. b. Now suppose you discover that your students don't know each other, and you decide to perfectly price discriminate. Once again, determine (1) how many students you will tutor; (2) what price you will charge; and (3) your weekly earnings from tutoring. Now suppose that your city requires all tutors to get a license, at a cost of \(\$ 1,300\) per year (\$25 per week). c. Does it make sense for you to buy this license and be a tutor if you must charge each student the same price? Explain. d. Does it make sense for you to buy the license and be a tutor if you can perfectly price discriminate? Explain.

Draw demand, \(M R, M C, A V C,\) and \(A T C\) curves that show a monopolist operating at a loss that would cause it to stay open in the short run, but exit the industry in the long run. Then, show how a technological advance that lowers only the monopolist's fixed costs could cause a change in its long-run exit decision.

Suppose a single-price monopoly's demand curve is given by \(P=20-4 Q,\) where \(P\) is price and \(Q\) is quantity demanded. Marginal revenue is \(M R=20-\) 8Q. Marginal cost is \(M C=Q^{2} .\) How much should this firm produce in order to maximize profit?

Draw demand, \(M R,\) and \(A T C\) curves that show a monopoly that is just breaking even.

In a certain large city, hot dog vendors are perfectly competitive, and face a market price of \(\$ 1.00\) per hot dog. Each hot dog vendor has the following total cost schedule: $$\begin{array}{cc} \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} & \text { Total cost } \\ \hline 0 & \$ 63 \\ 25 & 73 \\ 50 & 78 \\ 75 & 88 \\ 100 & 103 \\ 125 & 125 \\ 150 & 153 \\ 175 & 188 \\ 200 & 233 \end{array}$$ a. Add a marginal cost column to the right of the total cost column. (Hint: Don't forget to divide by the change in quantity when calculating \(M C .)\) b. What is the profit-maximizing quantity of hot dogs for the typical vendor, and what profit (loss) will he earn (suffer)? Give your answer to the nearest 25 hot dogs. One day, Zeke, a typical vendor, figures out that if he were the only seller in town, he would no longer have to sell his hot dogs at the market price of \(\$ 1.00\). Instead, he'd face the following demand schedule: $$\begin{array}{cc} \text { Price per Hot Dog } & \begin{array}{c} \text { Number of Hot } \\ \text { Dogs per Day } \end{array} \\ \hline>\$ 6.00 & 0 \\ 6.00 & 25 \\ 5.00 & 50 \\ 4.00 & 75 \\ 3.25 & 100 \\ 2.75 & 125 \\ 2.25 & 150 \\ 1.75 & 175 \\ 1.25 & 200 \end{array}$$ c. Add total revenue and marginal revenue columns to the table above. (Hint: Once again, don't forget to divide by the change in quantity when calculating MR.) d. As a monopolist with the cost schedule given in the first table, how many hot dogs would Zeke choose to sell each day? What price would he charge? e. A lobbyist has approached Zeke, proposing to form a new organization called "Citizens to Eliminate Chaos in Hot Dog Sales." The organization will lobby the city council to grant Zeke the only hot dog license in town, and it is guaranteed to succeed. The only problem is, the lobbyist is asking for a payment that amounts to \(\$ 200\) per business day as long as Zeke stays in business. On purely economic grounds, should Zeke go for it? (Hint: If you're stumped, re-read the section on rent-seeking activity.)
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