Part-2 Week-7
Aplia Homework: Production, Inputs, and Cost: Building Blocks for Supply Analysis
1. Inputs and outputs
Caroline's Performance Pizza is a small restaurant in San Francisco that sells gluten-free pizzas. Caroline's very tiny kitchen has barely enough room for the two ovens in which her workers bake the pizzas. Caroline signed a lease obligating her to pay the rent for the two ovens for the next year. Because of this, and because Caroline's kitchen cannot fit more than two ovens, Caroline cannot change the number of ovens she uses in her production of pizzas in the short run.
However, Caroline's decision regarding how many workers to use can vary from week to week because her workers tend to be students. Each Monday, Caroline lets them know how many workers she needs for each day of the week. In the short run, the wages paid to these workers are_______ costs, and the payments to lease the ovens are_______ costs.
Caroline's daily production schedule is presented in the following table.
Fill in the blanks to complete the Marginal Physical Product of Labour column for each worker.
| Number of Workers | Total Physical Product | Marginal Physical Product of Labour | |
|---|---|---|---|
| (Pizzas) | (Pizzas) | ||
| 0 | 0 | ||
| ___ | |||
| 1 | 70 | ||
| ___ | |||
| 2 | 120 | ||
| ___ | |||
| 3 | 160 | ||
| ___ | |||
| 4 | 190 | ||
| ___ | |||
| 5 | 200 | ||
On the following graph, plot Caroline's total physical product (TPP) curve, sometimes called a production function, using the green points (triangle symbol).
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.
Hint: Be sure to plot the first point at (0, 0).
Suppose that labour is Caroline's only variable cost and that she has a fixed cost of $10 per day and pays each of her workers $50 per day.
Use the orange points (square symbol) to plot Caroline's total cost curve on the following graph using the quantities from the preceding table.
True or False: The shape of the TPP reflects the “law” of diminishing marginal returns.
True
False
2. Total, average, and marginal product
Underground Sandwiches, a sandwich shop, has the following marginal physical product curve (labelled MPP) for its hourly production.
Note: Marginal values are sometimes plotted between integers (to indicate that they represent changes incurred in moving from one integer to the next), and sometimes they are plotted directly on the integers with which they are associated. For the context of this graph, they are plotted between integers. For example, if the marginal physical product from one unit of labour to two is x, this point is plotted at (1.5, x).
When labour increases from four to five workers, total physical product _______ by_______ per hour.
Use the orange points (square symbol) to plot the total physical product curve on the following graph. Assume that if there are no workers, Underground Sandwiches does not produce output.
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.
On the graph showing the marginal physical product (MPP) curve, use the purple points (diamond symbol) to plot the average physical product curve (APP) at one, two, three, four, and five workers.
The marginal physical product (MPP) curve and average physical product (APP) curve intersect at the________ of the_______ curve.
3. Graphing demand for labour (MRP) and computing the optimal quantity
A company operates in a perfectly competitive market, selling each unit of output for a price of $30 and paying the market wage of $285 per day for each worker it hires.
In the following table, complete the column for the marginal revenue product of labour (MRP) at each quantity of workers.
| Quantity of Labour | Total Physical Product | Marginal Physical Product of Labour | Marginal Revenue Product of Labour | |
|---|---|---|---|---|
| (Number of workers) | (Units of output) | (Units of output) | (Dollars) | |
| 0 | 0 | |||
| 16 | ___ | |||
| 1 | 16 | |||
| 15 | ___ | |||
| 2 | 31 | |||
| 14 | ___ | |||
| 3 | 45 | |||
| 11 | ___ | |||
| 4 | 56 | |||
| 8 | ___ | |||
| 5 | 64 | |||
Note: Marginal values are sometimes plotted between integers (to indicate that they represent changes incurred in moving from one integer to the next), and sometimes they are plotted directly on the integers with which they are associated. For the context of this graph, they are plotted between integers. For example, if the marginal physical product from one unit of labour to two is x, this point is plotted at (1.5, x).
On the following graph, use the blue points (circle symbol) to plot the firm's marginal revenue product of labour curve. Then, use the orange line (square symbols) to show the wage rate.
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.
Hint: Marginal values are sometimes plotted between integers (to indicate that they represent changes incurred in moving from one integer to the next), and sometimes they are plotted directly on the integers with which they are associated. For the context of this graph, they are plotted between integers. For example, when the number of workers increases from 0 to 1, the marginal revenue product for the first worker should be plotted with a horizontal coordinate of 0.5, the value halfway between 0 and 1.
The profit-maximizing quantity of labour at the market wage is_______.
4. The marginal rule for optimal input combination
Larry Green runs a surfing school on the North Shore of Oahu. He has two inputs: surfboards, which he rents from a local shop for $15 per day, and surfing instructors, whom he hires for $50 per day. Larry has figured out that the marginal revenue product (MRP) of the last instructor hired is $500, and the MRP of the last board used is $300.
Which of the following statements is correct?
Larry will optimize his input combination if he employs fewer instructors and uses more surfboards.
Larry currently employs the optimal combination of surfboards and instructors.
Larry will optimize his input combination if he employs more instructors and uses fewer surfboards.
5. Various measures of cost
Douglas Fur is a small manufacturer of fake-fur boots in Denver. The following table shows the company's total cost of production at various production quantities.
Fill in the remaining cells of the table.
| Quantity | Total Cost | Total Fixed Cost | Total Variable Cost | Marginal (Variable) Cost | Average Variable Cost | Average Cost | |
|---|---|---|---|---|---|---|---|
| (Pairs) | (Dollars) | (Dollars) | (Dollars) | (Dollars) | (Dollars per pair) | (Dollars per pair) | |
| 0 | 120 | ___ | ___ | — | — | ||
| ___ | |||||||
| 1 | 200 | ___ | ___ | ___ | ___ | ||
| ___ | |||||||
| 2 | 240 | ___ | ___ | ___ | ___ | ||
| ___ | |||||||
| 3 | 285 | ___ | ___ | ___ | ___ | ||
| ___ | |||||||
| 4 | 340 | ___ | ___ | ___ | ___ | ||
| ___ | |||||||
| 5 | 425 | ___ | ___ | ___ | ___ | ||
| ___ | |||||||
| 6 | 540 | ___ | ___ | ___ | ___ | ||
On the following graph, plot Douglas Fur’s average cost (AC) curve using the green points (triangle symbol). Next, plot its average variable cost (AVC) curve using the purple points (diamond symbol). Finally, plot its marginal (variable) cost (MVC) curve using the orange points (square symbol). (Hint: For AC and AVC, plot the points on the integer: For example, the average cost of producing one pair of boots is $200, so you should start your average cost curve by placing a green point at (1, 200). For marginal (variable) cost, plot the points between the integers: For example, the marginal (variable) cost of increasing production from zero to one pair of boots is $80, so you should start your marginal (variable) cost curve by placing an orange square at (0.5, 80).)
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.
6. Costs in the short run versus the long run
Ike's Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company's short-run average cost each month for various levels of production if it uses one, two, or three factories. (Note: QQ equals the total quantity of bikes produced by all factories.)
| Number of Factories | Average Cost | |||||
|---|---|---|---|---|---|---|
| (Dollars per bike) | ||||||
| QQ = 100 | QQ = 200 | QQ = 300 | QQ = 400 | QQ = 500 | QQ = 600 | |
| 1 | 280 | 120 | 80 | 160 | 320 | 640 |
| 2 | 460 | 220 | 80 | 80 | 220 | 460 |
| 3 | 640 | 320 | 160 | 80 | 120 | 280 |
Suppose Ike’s Bikes is currently producing 500 bikes per month in its only factory. Its short-run average cost is______ per bike.
Suppose Ike’s Bikes is expecting to produce 500 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using_________.
On the following graph, plot the three short-run average cost (SRACSRAC) curves for Ike’s Bikes from the previous table. Specifically, use the green points (triangle symbol) to plot its short-run average cost if it operates one factory (SRAC1SRAC1); use the purple points (diamond symbol) to plot its short-run average cost if it operates two factories (SRAC2SRAC2); and use the orange points (square symbol) to plot its short-run average cost if it operates three factories (SRAC3SRAC3). Finally, plot the long-run average cost (LRACLRAC) for Ike’s Bikes using the blue points (circle symbol).
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.
In the long run, over which range of output levels does Ike’s Bikes experience decreasing returns to scale?
More than 400 bikes per month
Between 300 and 400 bikes per month
Fewer than 300 bikes per month
7. Long-run cost relationships
The following graph shows the short-run average total cost curves and the long-run average total cost curve for a publishing firm. The five marked quantities indicate points of tangency between each short-run average total cost (ACAC) curve and the long-run average total cost (LRACLRAC) curve; for example, Q1Q1 marks the point of tangency between AC1AC1 and LRACLRAC.
The orange point on AC3AC3 indicates the firm's current output level in the short run (Q4Q4).
In the long run, if the firm decides to keep output at its initial level, what will it likely do?
Stay on AC3 but decrease to the point touching LRAC
Shift to operate on AC4
Shift to operate on AC2
Shut down
Over which range of output levels do you find economies of scale?
Greater than Q3
Q2 to Q4
0 to Q5
0 to Q3
0 to Q1
8. Cost-curve shifters
The following graph shows the average cost (AC) curve, average variable cost (AVC) curve, and average fixed cost (AFC) curve for Ana's Pizza Parlour when the retail price Ana pays for pizza dough, including sales tax, is $5 per large pizza.
Suppose the sales tax on pizza dough is removed, so the price of pizza dough decreases to $4 per large pizza.
In the following table, indicate how each curve is affected, if at all.
Cost
Effect on Cost and Curve
Average Cost ___________________________________.
Average Variable Cost ______________________________.
Average Fixed Cost ______________________________.
9. Producer theory with production indifference curve
Suppose a firm has two inputs: capital and labour. The following table shows how much labour the firm needs to produce 100, 200, or 300 units of output if it has 1, 2, 3, or 4 units of capital:
| Quantity Produced | Labour Input (Hours) | |||
|---|---|---|---|---|
| With 1 Unit of Capital | With 2 Units of Capital | With 3 Units of Capital | With 4 Units of Capital | |
| 100 | 55 | 20 | 10 | 5 |
| 200 | 80 | 40 | 25 | 15 |
| 300 | 90 | 55 | 35 | 20 |
On the following diagram, plot this firm's production indifference curves for 200 and 300 units of output. Specifically, use the purple points (diamond symbol) to plot the production indifference curve corresponding to 200 units of output; use the green points (triangle symbol) to plot the production indifference curve corresponding to 300 units of output.
Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. Points will snap to the quantities of labour.
Assume that the price of labour is $15 per hour, and the price of capital is $300 per unit. Given these input prices, the least expensive way to produce 100 units of output is to use______ of capital and_______ hours of labour.
Suppose the firm's production indifference curve corresponding to an output of 100 units can be approximated by the smooth curve, labelled “Q=100,” on the following graph.
Using the green line (triangle symbols), add the lowest budget line that the firm can attain at the given prices for capital and labour. Then use the black point (plus symbol) to identify the least-cost combination of labour and capital that can be used to produce an output level of 100.
10. Using production indifference curves to determine the least-cost combination of inputs
You are a department manager in a large web design firm, and you have an assignment to produce a customized website for a client in the next week. Your boss asks you to find the least costly way to produce the website.
In order to produce the website, you'll need to use computers and programmers. The production indifference curve on the following graph shows the combinations of computers and programmers that you can use to create the website in a week.
Which of the following are not combinations of programmers and computers that could produce the website within the time allotted? Check all that apply.
Three programmers and three computers
Four programmers and three computers
Two programmers and six computers
Four programmers and four computers
Each computer costs $400 per week, and each programmer costs $300 per week. Suppose your boss gives you a budget of $1,200 to spend on the project. (In other words, your boss wants the total cost of this project to equal $1,200.) On the previous graph, using the purple line (diamond symbol), plot the possible combinations of inputs you could afford—that is, plot your $1,200 budget line.
What should you tell your boss about completing the website in a week with a budget of $1,200?
“Sure, this won't be a problem.”
“That's very generous, but we don't need such a large budget to complete the project.”
“I can't complete the project by next week if that's all the money I can spend on it.”
The least-cost input combination is_________ and________, for a total cost of ______. (Hint: Calculate the cost of each of the blue points (circle symbols) on the production indifference curve on the previous graph.)
On the previous graph, use the green line (triangle symbol) to plot the budget line showing the possible combinations of computers and programmers you could use for your cost-minimizing budget. For example, if you've found that the least expensive option for completing the website costs $1,000, then you should plot a $1,000 budget line. Finally, use the black point (plus symbol) to identify the least-cost combination of computers and programmers that can be used to produce the level of output represented by the blue production indifference curve.
11. Historical vs analytical cost curves
The following graph shows the historical cost curve (black curve) and the analytical cost curves for both 1940 (purple curve) and the current year (orange curve) in the public utilities industry in the fictitious country of Cuytuodan. Suppose that both in 1940 and currently, only one large firm supplies utilities in Cuytuodan.
Based only on the historical cost curve, you cannot say with certainty that a larger firm can currently supply utilities to Cuytuodan more cheaply than smaller firms because of economies of scale.
True
False
Based on the shapes and positions of the analytical cost curves, in 1940 it was_______ , per unit of output, for small firms to supply utilities to Cuytuodan than for one large firm to do so. Currently, it is_______, per unit of output, for small firms to supply utilities to Cuytuodan than for to one large firm to do so.
