Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 3

Frances sells pencils in the perfectly competitive pencil market. Her output per day and her total cost are shown in the following table: $$ \begin{array}{|c|c|} \hline \text { Output per Day } & \text { Total Cost } \\ \hline 0 & \$ 1.00 \\ \hline 1 & 2.50 \\ \hline 2 & 3.50 \\ \hline 3 & 4.20 \\ \hline 4 & 4.50 \\ \hline 5 & 5.20 \\ \hline 6 & 6.80 \\ \hline 7 & 8.70 \\ \hline 8 & 10.70 \\ \hline 9 & 13.00 \\ \hline \end{array} $$ a. If the current equilibrium price in the pencil market is \(\$ 1.80,\) how many pencils will Frances produce, what price will she charge, and how much profit (or loss) will she make? Draw a graph to illustrate your answer. Your graph should be clearly labeled and should include Frances's demand, \(A T C, A V C, M C,\) and \(M R\) curves; the price she is charging; the quantity she is producing; and the area representing her profit (or loss). b. Suppose the equilibrium price of pencils falls to \(\$ 1.00\). Now how many pencils will Frances produce, what price will she charge, and how much profit (or loss) will she make? Show your work. Draw a graph to illustrate this situation, using the instructions in part (a). c. Suppose the equilibrium price of pencils falls to \(\$ 0.25 .\) Now how many pencils will Frances produce, what price will she charge, and how much profit (or loss) will she make?

Short Answer

Expert verified
a) When the price is $1.80, Frances must produce 4 pencils and will suffer a loss of $1.80. b) When the price falls to $1.00, she must produce 2 pencils and will incur a loss of $1.50. c) If the pencil price drops to $0.25, she should not produce any pencils, resulting in a loss of $1.00, which is her fixed cost.

Step by step solution

01

Calculate the ATC, AVC, and MC

First, calculate the Average Total Cost (ATC) by dividing the total cost by the quantity of pencils produced. Similarly, calculate the Average Variable Cost (AVC) and Marginal Cost (MC) by subtracting the cost of producing one less unit from the cost of producing the current quantity of units.
02

Find the best quantity to produce when price is $1.80

Considering the equilibrium price of $1.80, analyze the cost table and produce up to the quantity where the MC (Marginal Cost) does not exceed $1.80. The MC of producing the fifth pencil is higher than $1.80, hence Frances should produce and sell 4 pencils.
03

Calculate the profit/loss for price $1.80

Subtract the total cost of producing 4 pencils from the total revenue at a selling price of $1.80 each. So, the profit = (4 x $1.80) - $4.50 = $2.70 - $4.50 = -$1.80, indicating a loss of $1.80.
04

Determine quantity for price $1.00

Following the same process for the new equilibrium price of $1.00, Frances should produce up to the quantity where MC does not exceed $1.00. So, she should produce and sell 2 pencils.
05

Calculate the profit/loss for price $1.00

Again, subtract the total cost of producing 2 pencils from the total revenue at a selling price of $1.00 each. So, the profit = (2 x $1.00) - $3.50 = $2.00 - $3.50 = -$1.50, showing a loss of $1.50.
06

Determine quantity for price $0.25

For the new equilibrium price of $0.25, it seems that producing any pencils will result in a loss (since even the first pencil's MC is more than $0.25). Hence the quantity produced will be 0.
07

Calculate the profit/loss for the price $0.25

The revenue will be 0, and the loss equals to the fixed cost, which is $1.00.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Hedrick Smith was a foreign correspondent for the New York Times who lived in the Soviet Union in the \(1970 \mathrm{~s}\), a period when the country had a planned economy rather than a market system. In a book he wrote about everyday life in the Soviet Union, Smith made the following observations about shopping in Moscow: At first it seemed \(\ldots\) that the stores were pretty well stocked. Only as we began to shop in earnest \(\ldots\) did the Russian consumer's predicament really come through to me. First, we needed textbooks for our children \(\ldots\) and found that the sixth-grade textbooks had run out.... We tried to find ballet shoes for our 11 -year-old daughter... only to discover that in this land of ballerinas, ballet shoes size 8 were unavailable in Moscow.... I tried to find shoes for myself. They were out of anything in my size but sandals or flimsy, lightweight shoes that the clerk, with one look at me, recommended against buying. "They won't last," he admitted. a. Judging by Smith's observations, briefly explain whether the Soviet Union achieved allocative efficiency in the production of sixth-grade textbooks, ballet shoes, and men's shoes. b. Can we tell from these observations whether the Soviet Union achieved productive efficiency in the production of sixth-grade textbooks, ballet shoes, and men's shoes? Briefly explain.

(Related to the Don't Let This Happen fo You on page 418 ) Explain whether you agree with the following remark: According to the model of perfectly competitive markets, the demand curve for wheat should be a horizontal line. But this can't be true: When the price of wheat rises, the quantity of wheat demanded falls, and when the price of wheat falls, the quantity of wheat demanded rises. Therefore, the demand curve for wheat is not a horizontal line.

In \(2015,\) cocoa prices rose 13 percent from the previous year, the fourth straight year in which prices increased. However, by the end of 2016 cocoa prices fell. Edward George, the head of research at Ecobank, commented, "Everyone's like, wow. There's a lot of cocoa out there." Much of the world's supply of cocoa beans is grown in West Africa. a. Assume that the market for cocoa beans is perfectly competitive and was in long-run equilibrium in 2012 . Draw two graphs: one showing the world market for cocoa beans and one showing the market for the cocoa beans grown by a representative farmer. b. Assume that there was an increase in the worldwide demand for chocolate in \(2013 .\) In the graphs you drew in part (a), show the short-run effect of the demand increase. c. Explain why the supply of cocoa beans increased and the price decreased in \(2016 .\) Show the effect of this increase in supply on the graphs you drew in part (b).

Explain whether each of the following is a perfectly competitive market. For each market that is not perfectly competitive, explain why it is not. a. Corn farming b. Coffee shops c. Automobile manufacturing d. New home construction

A columnist for the Wall Street Journal discussed the fact that some firms were buying existing drilling operations in Canadian oil sands regions. These operations would not have been profitable to build from scratch but were profitable to operate given that they were already built because, as the columnist said, "The key is the distinction between fixed and variable costs. While the fixed investment in new oil sands projects is prohibitive, variable costs can be in the low \(\$ 20\) range per barrel." The columnist estimated that the fixed cost of a new oil sands drilling operation could be \(\$ 95\) per barrel. At the time the column was written, the price of oil was about \(\$ 50\) per barrel. a. Assuming that variable cost of an existing oil sands operation is \(\$ 20\) per barrel and the price of oil is \(\$ 50\) per barrel, how much were the companies selling these drilling operations losing per barrel? b. At a price of \(\$ 50\) per barrel, were the companies buying the existing drilling operations earning a profit of \(\$ 30\) per barrel? If not, explain what information we would need to calculate their profit.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free