Part-2   Week-8 

Aplia Homework: Output, Price, and Profit: The Importance of Marginal Analysis

1. Accounting versus economic profit

In a given year, a marketing firm has the following costs: $560,000 in wages and salaries paid to employees; $74,000 in rental payments for office space; and $170,000 for office supplies, advertising, and utilities. In addition, Yaakov, the owner of the firm, works for the firm full time (and is not paid a salary, since he receives the firm's profits). If he did not work for the marketing firm, Yaakov could earn $120,000 per year working as a marketing manager for another firm.

For each possible amount of total revenue, fill in the accounting profit and economic profit of the marketing firm.

2. Calculating marginal revenue from a linear demand curve

The blue curve on the following graph represents the demand curve facing a firm that can set its own prices.

Use the graph input tool to help you answer the following questions. You will not be graded on any changes you make to this graph.

Note: Once you enter a value in the white field, the graph and any corresponding amounts in each grey field will change accordingly.

On the preceding graph, change the number found in the Quantity demanded field to determine the prices that correspond to the production of 0, 10, 20, 25, 30, 40, or 50 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results.

Calculate the total revenue if the firm produces 10 versus 9 units. Then, calculate the marginal revenue of the 10th unit produced.

The marginal revenue of the 10th unit produced is_______.

Calculate the total revenue if the firm produces 20 versus 19 units. Then, calculate the marginal revenue of the 20th unit produced.

The marginal revenue of the 20th unit produced is_______.

Based on your answers from the previous question, and assuming that the marginal revenue curve is a straight line, use the black line (plus symbol) to plot the firm's marginal revenue curve on the following graph. (Round all values to the nearest multiple of 10.)

Note: Marginal revenue is ordinarily plotted between integers; in this problem, you will plot MR right at integer values. When the distance from one unit to the next is very small—as in this graph—there is no noticeable difference in the two plotting methods.

Comparing your total revenue graph to your marginal revenue graph, you can see that total revenue is ________ at the output at which marginal revenue is equal to zero.

3. Profit versus total revenue

A firm has total revenue (TR) and total cost (TC) curves as shown on the following diagram. To complete the graph, you will have to illustrate two distances with line segments.

Determine the quantity of output that generates the maximum profit. Use the green points (triangle symbol) to indicate the amount of profit at this quantity of output. Then, determine the quantity of output that generates the maximum total revenue. Use the purple points (diamond symbol) to indicate the amount of revenue at this quantity of output.

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

The maximum profit this firm can earn is_______, while the maximum total revenue it can earn is_______.

4. Marginal analysis and profit maximization

Suppose Crystal gives haircuts on Saturdays to make extra money. She is the only person in town cutting hair on Saturdays, so she has some market power. Assume that she does not incur fixed costs and that the only significant variable cost to Crystal in giving haircuts is her time. As she gives more haircuts, Crystal must increasingly forgo other valuable Saturday activities. For example, if she gives one haircut, she forgoes reading the paper after breakfast. If she gives two haircuts, she gives up reading the paper, sleeping an extra half-hour, and so on.

Crystal's clients are a varied group willing to pay between $18.00 and $30.00 for a haircut. Assume that Crystal cannot price discriminate—that is, charge different clients different prices. If Crystal charges $30.00 per haircut, she will have one client per week; if she charges $27.00, she will have two; if she charges $24.00, three, and so forth. The following table contains data on the revenues and costs of Crystal's haircut business as a function of her price–quantity choice. (The costs are based on the value of Crystal's alternative activities, in dollar terms. For example, the total cost of the first haircut is $3—the value Crystal places on reading the newspaper after breakfast.) Also, marginal profit is the additional profit Crystal earns from producing one more unit of output. Marginal profit is positive when a rise in output increases total profit and negative when a rise in output causes total profit to fall.

Fill in the missing cells of the table and then use them to answer the questions that follow.

On the following graph, use the blue points (circle symbol) to plot Crystal's total revenue curve, use the orange points (square symbol) to plot her total cost curve, and use the purple points (diamond symbol) to plot her total profit curve.

Note: Be sure to graph from left to right, starting with zero haircuts and ending with five. Line segments will automatically connect the points.

On the following graph, use the blue points (circle symbol) to plot Crystal's marginal revenue (MR) curve, and then use the orange points (square symbol) to plot her marginal cost (MC) curve for the first five haircuts.

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. On the following graph, be sure to plot marginal values directly on the integers with which they are associated. For example, if Crystal's marginal cost of increasing her production from one haircut to two haircuts is x, then you would plot a point at (2, x). Line segments will automatically connect the points.

Crystal maximizes her profit by serving _______ per week and charging_______ per haircut.

If Crystal gave more haircuts than her optimal quantity of haircuts, which of the following statements would be true? Check all that apply.

            Crystal's total profit (total revenue minus total cost) would decline.

            Crystal's marginal profit would be negative.

            Crystal's marginal revenue would be less than her marginal cost.

5. Interpreting MR and MC

A hair salon that provides haircuts has determined that it faces the daily revenue and cost data shown in the following table.

Complete the following table by determining the marginal revenue (MR) and marginal cost (MC) associated with changes in output from 0 to 15, 15 to 30, and 30 to 45 haircuts per day, and enter your answers in the appropriate column.

Hint: Remember that marginal revenue (MR) is defined as the change in total revenue divided by the change in output.

Suppose the hair salon is currently doing 15 haircuts per day. As an economist, what advice would you give Eric, the owner of the hair salon?

            "You should perform fewer haircuts per day, because the marginal revenue from performing an additional haircut is smaller than the marginal cost."

            "You should perform more haircuts per day, because the marginal revenue from performing an additional haircut is larger than the marginal cost."

            "You should perform 45 haircuts per day, because at that quantity, total revenue minus total cost is positive."

            "You should perform the number of haircuts that yields the highest total revenue."

6. Making "how much" decisions

Brian provides cleaning services in his apartment complex. He cleans one apartment per hour, so, working a full day, Brian can clean a total of 8 apartments. The next best use of Brian's time involves online freelance work, which he can pick up at any time for $8 per hour. The following table contains information on Brian's total and marginal costs of cleaning apartments as well as information on his total and marginal benefits from cleaning apartments.

To clean the first apartment, Brian incurs an opportunity cost of $8 (for the hour of earnings forgone) and explicit costs of $2 for replacing cleaning supplies and upkeep of his equipment for a total cost of $10. Since Brian's total cost is zero when he doesn't clean, the marginal cost of cleaning the first apartment is $10. The marginal cost of cleaning the second apartment is $12—he incurs an additional opportunity cost of $8 and an additional $4 in costs for supplies and equipment upkeep. The total cost of cleaning two apartments is therefore $10 for the first apartment plus an additional $12 for the second, or $22.

Since the opportunity cost of tenants' time varies, so too does their willingness to pay for cleaning. Brian's marginal benefit from cleaning an apartment depends on the tenants' willingness to pay. Assume that the occupant of the first apartment will pay Brian $36 to clean the apartment. Brian's marginal benefit of cleaning the first apartment is therefore $36. Consider that the occupant of the second apartment also has a relatively high opportunity cost of cleaning compared to most other occupants and will pay Brian $34 to clean the apartment. Brian's marginal benefit of cleaning the second apartment is therefore $34. His total benefit from cleaning two apartments is equal to the marginal benefit from the second apartment ($34) plus the marginal benefit of the first ($36), or $70.

Complete the following table by entering the missing values.

Using the preceding table, plot Brian's marginal cost and marginal benefit curves for cleaning apartments. Be sure to plot on the integers. For example, the marginal cost of the first apartment is $10, so the first point on your marginal cost curve should be (1, 10).

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

Brian's net benefit from cleaning the fifth apartment is ______, and his total net benefit from cleaning five apartments is _________.

Brian's net benefit from cleaning the eighth apartment is _______, and his total net benefit from cleaning eight apartments is ­­_______.

For Brian, the optimal quantity of apartments to clean each day is _______.

7. How a change in fixed costs affects the profit-maximizing quantity

Larry owns and operates a hot dog stand in downtown Houston. In order to operate his hot dog stand, regardless of the number of hot dogs sold, Larry must purchase a permit from the local government in Houston. Larry's initial profit hill is plotted in green (triangle symbols) on the following graph.

Suppose the price Larry must pay for a permit decreases by $50 per day.

On the following graph, use the purple diamond symbols to plot Larry's new profit hill, for 0, 10, 20, 30, 40, 50, 60, and 70 hot dogs, after the decrease in the price of a permit (with all other factors remaining constant).

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

Based on the graph, you can tell that Larry initially faces a fixed cost of _______ per day.

Initially, Larry's profit-maximizing level of output is ______  hot dogs per day. After the price of a permit falls, Larry's profit-maximizing level of output is _______   hot dogs per day.

8. The relationship between marginal and average costs

Consider the following scenario to understand the relationship between marginal and average values. Suppose Kevin is a professional basketball player, and his game log for free throws can be summarized in the following table.

Fill in the columns with Kevin's free-throw percentage for each game and his overall free-throw average after each game.

On the following graph, use the orange points (square symbol) to plot Kevin's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot his overall average free-throw percentage after each game.

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

You can think of the result in any one game as being Kevin's marginal free-throw percentage. Based on your previous answer, you can deduce that when Kevin's marginal free-throw percentage is above the average, the average must be _______.

You can now apply this analysis to production costs. For a U-shaped average total cost curve, when the marginal cost curve is below the average total cost curve, the average total cost must be _________. Also, when the marginal cost curve is above the average total cost curve, the average total cost must be _________. Therefore, the marginal cost curve intersects the average total cost curve ______________.