Long free-response question

Hiring at a juice stand

Units 3 and 5
10 points
About 25 minutes

You can use a calculator on this question, just like on exam day.

A long question with several lettered parts built around one scenario, often a firm in a particular market structure, and it can pull in other units such as a labor market or a payoff matrix. You identify outcomes, explain them, do a calculation, and describe a correctly labeled graph that shows the situation and how a change affects it. On the exam: Question 1 of 3 in Section II (60 minutes including a 10-minute reading period; 33.35% of the exam score); 10 points, half of the section score. About 25 minutes suggested. Four-function calculator allowed.

The question and its sources

Sunny's Juice sells bottles of juice in a perfectly competitive market at a price of $5 per bottle. It hires workers in a perfectly competitive labor market at the market wage of $60 per day. Labor is its only variable input. The table shows Sunny's daily output.

Table 1. Sunny's Juice daily production

Number of workers	Total output (bottles per day)
0	0
1	20
2	38
3	54
4	67
5	75
6	79

Source: Hypothetical data

Suggested time: 25 minutes

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Part (a)

1 point

Calculate the marginal revenue product of the third worker. Show your work.

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Part (b)

1 point

Identify the number of workers Sunny's will hire to maximize profit.

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Part (c)

1 point

Explain why Sunny's would not hire a fifth worker.

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Part (d)

1 point

Identify the worker with whom diminishing marginal returns begin. Explain using the data.

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Part (e)

2 points

Describe correctly labeled side-by-side graphs of the labor market and of Sunny's Juice. Show (i) the market wage of $60 and the market quantity of labor; (ii) the labor supply curve Sunny's faces, labeled S; (iii) Sunny's MRP curve; and (iv) the number of workers Sunny's hires.

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Part (f)

1 point

Suppose the price of juice rises to $8 per bottle, while the wage stays at $60. Identify the number of workers Sunny's will now hire to maximize profit. Show your work.

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Part (g)

1 point

Return to the original price of $5. Suppose a new juicer increases the marginal product of every worker. Identify the effect on Sunny's MRP curve. Explain.

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Part (h)

1 point

Using the original price of $5 and wage of $60, calculate the marginal cost of a bottle of juice when Sunny's hires the third worker. Show your work.

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Part (i)

1 point

Using the original price of $5 and wage of $60, calculate the marginal cost per bottle of the output added by the fourth worker and of the output the fifth worker would add. Use these to show that Sunny's hiring decision in part (b) is consistent with the profit-maximizing rule for output, MR = MC.

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