6.E: Production and Cost Structure of the Firm (Exercises)
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7.1: Explicit and Implicit Costs, and Accounting and Economic Profit
Self-Check Questions
Q1
A firm had sales revenue of \(\$1\) million last year. It spent \(\$600,000\) on labor, \(\$150,000\) on capital and \(\$200,000\) on materials. What was the firm’s accounting profit?
Q2
Continuing from Q1, the firm’s factory sits on land owned by the firm that could be rented out for \(\$30,000\) per year. What was the firm’s economic profit last year?
Review Questions
Q3
What are explicit and implicit costs?
Q4
Would an interest payment on a loan to a firm be considered an explicit or implicit cost?
Q5
What is the difference between accounting and economic profit?
Critical Thinking Questions
Q6
Small “Mom and Pop firms,” like inner city grocery stores, sometimes exist even though they do not earn economic profits. How can you explain this?
Problems
Q7
A firm is considering an investment that will earn a \(6\%\) rate of return. If it were to borrow the money, it would have to pay \(8\%\) interest on the loan, but it currently has the cash, so it will not need to borrow. Should the firm make the investment? Show your work.
Solution
S1
\[\begin{align*} \text{Accounting profit} &= \text{total revenues minus explicit costs}\\ &= \$1,000,000 - (\$600,000 + \$150,000 + \$200,000)\\ &= \$50,000 \end{align*}\]
S2
\[\begin{align*} \text{Economic profit} &= \text{accounting profit minus implicit cost}\\ &= \$50,000 - \$30,000\\ &= \$20,000 \end{align*}\]
7.2: The Structure of Costs in the Short Run
Self-Check Questions
Q1
The WipeOut Ski Company manufactures skis for beginners. Fixed costs are \(\$30\). Fill in Table below for total cost, average variable cost, average total cost, and marginal cost.
| Quantity | Variable Cost | Fixed Cost | Total Cost | Average Variable Cost | Average Total Cost | Marginal Cost |
|---|---|---|---|---|---|---|
| 0 | 0 | $30 | ||||
| 1 | $10 | $30 | ||||
| 2 | $25 | $30 | ||||
| 3 | $45 | $30 | ||||
| 4 | $70 | $30 | ||||
| 5 | $100 | $30 | ||||
| 6 | $135 | $30 |
Q2
Based on your answers to the WipeOut Ski Company in Q1, now imagine a situation where the firm produces a quantity of \(5\) units that it sells for a price of \(\$25\) each.
- What will be the company’s profits or losses?
- How can you tell at a glance whether the company is making or losing money at this price by looking at average cost?
- At the given quantity and price, is the marginal unit produced adding to profits?
Review Questions
Q3
What is the difference between fixed costs and variable costs?
Q4
Are there fixed costs in the long-run? Explain briefly.
Q5
Are fixed costs also sunk costs? Explain.
Q6
What are diminishing marginal returns as they relate to costs?
Q7
Which costs are measured on per-unit basis: fixed costs, average cost, average variable cost, variable costs, and marginal cost?
Q8
How is each of the following calculated: marginal cost, average total cost, average variable cost?
Critical Thinking Questions
Q9
A common name for fixed cost is “overhead.” If you divide fixed cost by the quantity of output produced, you get average fixed cost. Supposed fixed cost is \(\$1,000\). What does the average fixed cost curve look like? Use your response to explain what “spreading the overhead” means.
Q10
How does fixed cost affect marginal cost? Why is this relationship important?
Q11
Average cost curves (except for average fixed cost) tend to be U-shaped, decreasing and then increasing. Marginal cost curves have the same shape, though this may be harder to see since most of the marginal cost curve is increasing. Why do you think that average and marginal cost curves have the same general shape?
Problems
Q12
Return to Figure 7.2.1. What is the marginal gain in output from increasing the number of barbers from \(4\) to \(5\) and from \(5\) to \(6\)? Does it continue the pattern of diminishing marginal returns?
Q13
Compute the average total cost, average variable cost, and marginal cost of producing \(60\) and \(72\) haircuts. Draw the graph of the three curves between \(60\) and \(72\) haircuts.
Solution
S1
| Quantity | Variable Cost | Fixed Cost | Total Cost | Average Variable Cost | Average Total Cost | Marginal Cost |
|---|---|---|---|---|---|---|
| 0 | 0 | $30 | $30 | - | - | |
| 1 | $10 | $30 | $40 | $10.00 | $40.00 | $10 |
| 2 | $25 | $30 | $55 | $12.50 | $27.50 | $15 |
| 3 | $45 | $30 | $75 | $15.00 | $25.00 | $20 |
| 4 | $70 | $30 | $100 | $17.50 | $25.00 | $25 |
| 5 | $100 | $30 | $130 | $20.00 | $26.00 | $30 |
| 6 | $135 | $30 | $165 | $22.50 | $27.50 | $35 |
S2
- Total revenues in this example will be a quantity of five units multiplied by the price of \(\$25/unit\), which equals \(\$125\). Total costs when producing five units are \(\$130\). Thus, at this level of quantity and output the firm experiences losses (or negative profits) of \(\$5\).
- If price is less than average cost, the firm is not making a profit. At an output of five units, the average cost is \(\$26/unit\). Thus, at a glance you can see the firm is making losses. At a second glance, you can see that it must be losing \(\$1\) for each unit produced (that is, average cost of \(\$26/unit\) minus the price of \(\$25/unit\)). With five units produced, this observation implies total losses of \(\$5\).
- When producing five units, marginal costs are \(\$30/unit\). Price is \(\$25/unit\). Thus, the marginal unit is not adding to profits, but is actually subtracting from profits, which suggests that the firm should reduce its quantity produced.
7.3: The Structure of Costs in the Long Run
Self-Check Questions
Q1
Return to the problem explained in Table 7.3.1 and Table 7.3.2. If the cost of labor remains at \(\$40\), but the cost of a machine decreases to \(\$50\), what would be the total cost of each method of production? Which method should the firm use, and why?
Q2
Suppose the cost of machines increases to \(\$55\), while the cost of labor stays at \(\$40\). How would that affect the total cost of the three methods? Which method should the firm choose now?
Q3
Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than \(2.5\) times the quantity produced at the bottom of the long-run average cost curve. What do you expect will happen to the domestic auto industry in the long run?
Review Questions
Q4
What shapes would you generally expect each of the following cost curves to have: fixed costs, variable costs, marginal costs, average total costs, and average variable costs?
Q5
What is a production technology?
Q6
In choosing a production technology, how will firms react if one input becomes relatively more expensive?
Q7
What is a long-run average cost curve?
Q8
What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?
Q9
What shape of a long-run average cost curve illustrates economies of scale, constant returns to scale, and diseconomies of scale?
Q10
Why will firms in most markets be located at or close to the bottom of the long-run average cost curve?
Critical Thinking Questions
Q11
It is clear that businesses operate in the short run, but do they ever operate in the long run? Discuss.
Q12
How would an improvement in technology, like the high-efficiency gas turbines or Pirelli tire plant, affect the long-run average cost curve of a firm? Can you draw the old curve and the new one on the same axes? How might such an improvement affect other firms in the industry?
Q13
Do you think that the taxicab industry in large cities would be subject to significant economies of scale? Why or why not?
Problems
Q14
A small company that shovels sidewalks and driveways has \(100\) homes signed up for its services this winter. It can use various combinations of capital and labor: lots of labor with hand shovels, less labor with snow blowers, and still less labor with a pickup truck that has a snowplow on front. To summarize, the method choices are:
Method 1: \(50\) units of labor, \(10\) units of capital
Method 2: \(20\) units of labor, \(40\) units of capital
Method 3: \(10\) units of labor, \(70\) units of capital
If hiring labor for the winter costs \(\$100/unit\) and a unit of capital costs \(\$400\), what production method should be chosen? What method should be chosen if the cost of labor rises to \(\$200/unit\)?
Solution
S1
The new table should look like this:
| Labor Cost | Machine Cost | Total Cost | |
|---|---|---|---|
| Cost of technology 1 | 10 × $40 = $400 | 2 × $50 = $100 | $500 |
| Cost of technology 2 | 7 × $40 = $280 | 4 × $50 = $200 | $480 |
| Cost of technology 3 | 3 × $40 = $120 | 7 × $50 = $350 | $470 |
The firm should choose production technology 3 since it has the lowest total cost. This makes sense since, with cheaper machine hours, one would expect a shift in the direction of more machines and less labor.
S2
| Labor Cost | Machine Cost | Total Cost | |
|---|---|---|---|
| Cost of technology 1 | 10 × $40 = $400 | 2 × $55 = $110 | $510 |
| Cost of technology 2 | 7 × $40 = $280 | 4 × $55 = $220 | $500 |
| Cost of technology 3 | 3 × $40 = $120 | 7 × $55 = $385 | $505 |
The firm should choose production technology 2 since it has the lowest total cost. Because the cost of machines increased (relative to the previous question), you would expect a shift toward less capital and more labor.
S3
This is the situation that existed in the United States in the 1970s. Since there is only demand enough for \(2.5\) firms to reach the bottom of the average cost curve, you would expect one firm will not be around in the long run, and at least one firm will be struggling.