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Microeconomics

Austan Goolsbee, Steven Levitt, Chad Syverson

Chapter 7

Costs - all with Video Answers

Educators

Chapter Questions

05:20

Problem 2

Chris owns his own business restoring antique cars. Last year, he restored 24 cars, which he sold for $\$ 1,100,000$.
The parts and supplies necessary for the restoration totaled $\$ 400,000 .$ He paid $\$ 360,000$ to his six employees and a salary of $\$ 110,000$ to himself. The rent and utilities on his building were $\$ 80,000$. Recently, Chris received an offer to work as Jay Leno's personal auto restorer, at a salary of $\$ 275,000 .$ Chris also received a $\$ 180,000$ offer to host a car-related reality TV show for the Discovery Channel. Chris can only work one job.
a. What is Chris's accounting cost? His accounting profit?
b. What is Chris's economic cost? His economic profit?
c. Compare what Chris earns in his current job (both his salary and his company's accounting profit) to his best outside offer. Does the figure you calculated look familiar? Does it shed any light on the meaning of economic profit?

Karan Sood
Karan Sood
Numerade Educator
06:06

Problem 3

Who doesn't love kicking back after work with a snack and a good show? Everyone loves some free time $\ldots$ but, of course, time isn't free! In the past 10 years, ridesharing services like Uber have become wildly popular. People who need to get from $\mathrm{A}$ to $\mathrm{B}$ value the ability to connect with a driver rapidly, rather than waiting for a scarce taxicab. And ordinary people (with a nice enough car) can earn a few extra bucks giving rides, working as little or as much as they please. Today, an estimated 2 million people drive for Uber, often evenings and weekends after they're finished the day at a full-time job. Explain how the growth of Uber reflects the way in which ride sharing has altered the opportunity cost of leisure.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
06:14

Problem 4

Philo T. Farmsworth is a corn farmer with a 40 -acre tract of land. Each acre can produce 100 bushels of corn. The cost of planting the tract in corn is $\$ 20,000,$ and the cost of harvesting the corn is $\$ 10,000 .$ In May, when corn is selling for $\$ 10$ per bushel, Philo plants his crop. By September, the price of corn has fallen to $\$ 2$ per bushel. What should Philo do? Explain, assuming that there are no costs involved with bringing the corn to market to sell.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
02:43

Problem 5

Each year on January $1,$ millions of Americans, having made New Year's resolutions to lose weight and get in shape, purchase annual gym memberships. A CNN survey recently suggested that nearly $30 \%$ of all New Year's resolutions are abandoned by February $1 ; 80 \%$ by July. In other words, millions of people buy expensive gym memberships and then fail to use them. Does this indicate that they fell victim to the sunk cost fallacy? Or, does it suggest that they well understand the nature of sunk costs? Explain your answer.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
04:52

Problem 6

In which of the following situations are costs sunk?
a. A drug company spends $\$ 20$ million to test the effectiveness of a new replacement drug for insulin, only to find
out it is ineffective.
b. AB-Inbev spends $\$ 15$ million to develop and advertise a new mango-wheat beer that few people enjoy.
c. A Kansas farmer wants to open a winery; she spends $\$ 600,000$ to buy farmland only to discover that the weather is too extreme to grow finicky grapes. She can resell the land to a wheat farmer for $\$ 450,000$.
d. Lockton, a risk-management company, pays a $\$ 10,000$ signing bonus to a new employee who turns out to be unreliable.
e. You purchase a $\$ 150$ ticket to a nighttime concert, only to have an instructor surprise you with a demanding assignment due the same evening.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
03:33

Problem 7

Karam recently opened a bar and grill. The costs associated with his new business are as follows:
a. $\$ 300,000$ to build the restaurant
b. $\$ 30,000$ for a liquor license
c. $\$ 50,000$ on furniture and kitchenware
d. 2 cooks who will each be paid $\$ 5,000$ per month
e. 5 waiters who will each be paid $\$ 3$ per hour plus tips
Which of Karam's costs are fixed, and which are variable? Explain.

Karan Sood
Karan Sood
Numerade Educator
04:55

Problem 8

Amanda owns a toy manufacturing plant with the production function $Q=100 L-3,000$, where $L$ is hired labor hours. Assume that Amanda has no fixed costs.
a. Rearrange Amanda's production function to show how many workers Amanda would have to hire to produce a given level of output. In other words, isolate $L$ on the left-hand side, expressing $L$ as a function of $Q$.
b. Because Amanda has no fixed costs, all her costs derive from paying workers. In other words, $T C=w \times L$. Substitute your answer from (a) into this equation to find Amanda's total cost function.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
03:50

Problem 9

Roy builds furniture in his North Carolina workshop. The cost of producing various numbers of bookstands is given
in the table below:
Complete the table. Then graph the total, fixed, and variable cost curves.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
08:49

Problem 10

A Toyota Corolla costs $\$ 18,700$ and has average highway fuel economy of 36 miles per gallon (mpg). A Toyota Prius costs $\$ 23,700$ and offers average highway fuel economy of $50 \mathrm{mpg}$.
a. Assuming gas costs $\$ 2.75$ per gallon, generate total cost equations as a function of miles driven for each of these cars. Identify the fixed and variable costs.
b. How many miles do you have to drive before the two cars have the same total cost?
c. You plan on holding on to your next car for 100,000 miles. You estimate that you can sell a used Corolla with 100,000 miles for $\$ 4,400$; a used Prius with 100,000 miles is worth $\$ 7,800$. If money is the only thing that matters to you, should you buy the Corolla or the Prius?

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
02:57

Problem 11

Consider the costs for Gisela's cupcake business:
Re-create the table above with columns showing Gisela's variable cost, average total cost, average fixed cost, and average variable cost.

Karan Sood
Karan Sood
Numerade Educator
06:01

Problem 12

Daniel's Midland Archers (DMA) makes children's wooden practice arrows. Draw a set of representative short-run cost curves for DMA. Include average variable cost, average fixed cost, average total cost, and marginal cost.
a. Suppose that Congress imposes a 39 -cent excise tax on each children's wooden practice arrow DMA sells. Illustrate the effects of this tax on the cost curves of DMA. Which curves shift and which do not?
b. Suppose that the city where DMA produces arrows increases the annual property tax on DMA's factory from $\$ 80,000$ to $\$ 150,000$. Illustrate the effects of this tax on the cost curves of DMA. Which curves shift and which
do not?

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
01:34

Problem 13

A firm's total cost curve is
$$\begin{array}{l}
T C=Q^{3}-60 Q^{2}+910 Q+150 \\
3 Q^{2}-120 Q+910
\end{array}$$
a. Find the firm's fixed cost, variable cost, average total cost, and average variable cost.
b. Find the output level at which average variable cost is minimized.

Andrew Davis
Andrew Davis
Numerade Educator
07:34

Problem 14

You are the CEO of a major producer of funnel cakes. Your cost accountant has provided you with a table describing your cost structure, but you have inadvertently dripped cooking grease on it and most of the table is illegible. Reconstruct the table below, given the remaining legible numbers:

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
02:42

Problem 15

True or false: Average variable cost reaches its minimum point at a lower level of output than average total costs.
Explain your answer, using a graph of average and marginal costs to illustrate.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
03:03

Problem 16

Suppose a firm has the following production function: $Q=2 K L$. The marginal product of capital for this production function is $2 L,$ and the marginal product of labor is $2 K .$ If capital rents for $\$ 100$ per unit per day, labor can be hired for $\$ 200$ per unit per day, and the firm is minimizing costs,
a. Find the total cost of producing 60 units of output.
b. Suppose you want to determine the cost of producing the more general $q$ units of output. Using the same set of procedures you followed in (a), but a more general $Q$ instead of $60,$ find this firm's total cost function, which expresses total cost as a function of $Q$.
c. Divide the total cost function you found in (b) by $Q$ to determine this firm's average cost function.

Crystal Wang
Crystal Wang
Numerade Educator
05:29

Problem 17

You run a specialty bicycle company, which produces a limited quantity of extremely tricked out racing bikes. Consider the following graph, which illustrates the short-run average total cost curves corresponding to three possible plant sizes: small, medium, and large.
a. If you wanted to produce 900 bikes, which plant size should you choose, and why? What if you wanted to produce 1,100 instead?
b. If you wanted to produce 2,100 bikes, which plant size should you choose, and why? What if you wanted to produce just $1,900 ?$
c. Darken the long-run average total cost curve your specialty bicycle company faces.

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
03:37

Problem 18

Suppose an increase in the minimum wage alters the cost of producing fast-food hamburgers. Show what happens to McDonald's long-run expansion path as a result of this wage increase. Does McDonald's alter its mix of inputs? What happens to McDonald's costs?

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
03:39

Problem 19

A builder of custom motorcycles must choose between operating out of one garage or two. When the builder operates out of one garage, its average total cost of production is given by$$A T C_{1}=Q^{2}-6 Q+14.$$If it operates out of two garages, its average total cost of production is given by $$A T C_{2}=Q^{2}-10 Q+30.$$ What does this firm's LATC look like? Can you describe it as a function?

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
07:20

Problem 20

Suppose that a firm has the following Cobb-Douglas production function: $$Q=12 K^{0.75} L^{0.25} .$$
a. What must its long-run total cost curve look like? Its long-run average total cost curve?
b. How do your answers to part (a) change if the firm's production function is $$Q=K L ?$$

Jonathan Tapiwa
Jonathan Tapiwa
Numerade Educator
07:24

Problem 21

Peter's Pipers produces plumbing pipe. The long-run total cost of Peter's pipes is $L T C=$
$$20,000 Q-200 Q^{2}+Q^{3},$$ where $Q$ is measured as thousands of feet of piping. The long-run marginal cost of Peter's pipes is given as $$L M C=20,000-400 Q+3 Q^{2}.$$
a. Divide total cost by $Q$ to obtain Peter's long-run average cost of producing pipe.
b. Exploit the relationship between $L M C$ and $L A C$ to find the quantity where $L A C$ is at a minimum.
c. What is the lowest possible average cost at which Peter can produce pipe?
d. Over what range of output does Peter's Pipers experience economies of scale? Over what range of output does Peter's Pipers experience diseconomies of scale?

Suzanne W.
Suzanne W.
Numerade Educator
13:06

Problem 22

Tyson Chicken produces both thighs and wings. When it produces 150 thighs and no wings, its total cost is $\$ 600$. When Tyson produces 150 wings and no thighs, its total cost is $\$ 400$. And when Tyson produces both 150 thighs and 150 wings jointly, its total costs are $\$ 900$.
a. Show that, for an output level of 150 thighs and 150 wings, Tyson experiences economies of scope.
b. What is the likely source of Tyson's economies of scope?

Robert Daugherty
Robert Daugherty
Numerade Educator