The Production Function

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AP Microeconomics › The Production Function

Questions 1 - 10
1

A small factory produces assembled toolkits (single output) using labor as the variable input; the assembly line (capital) is fixed. Based on the production data shown, what is the marginal product of the 6th worker?

Table: Total Product (TP) of Toolkits

Labor (L), workersTotal Product (TP), toolkits/day
00
13
28
314
419
523
626
728

5 toolkits per day

3 toolkits per day

6 toolkits per day

4 toolkits per day

26 toolkits per day

Explanation

This question focuses on the production function and the concept of marginal product of labor in AP Microeconomics. Marginal product (MP) is the additional output from hiring one more worker, and diminishing marginal returns refer to the stage where each additional worker adds less output than the previous one due to fixed capital. Using the provided table, we calculate MP for each worker to understand the pattern. The marginal product of the 6th worker is 26 - 23 = 3 toolkits per day, as shown by the change in TP from 5 to 6 workers. Don't confuse marginal product with average product, which is TP divided by labor (e.g., AP at 6 workers is 26/6 ≈4.33). To compute marginal product, always use the formula MP = ΔTP / ΔL, where ΔL is usually 1. Look for diminishing returns by observing when MP starts declining as labor increases while capital is fixed.

2

A landscaping company produces completed yards per day using labor (workers) as the variable input; equipment is fixed. Based on the production data shown in the table, what is the marginal product of the 5th worker?

Labor (L)Total Product (TP), yards/day
00
13
27
312
416
519
621
Question graphic

$2$ yards/day

$3.8$ yards/day

$4$ yards/day

$3$ yards/day

$19$ yards/day

Explanation

This question tests your ability to calculate the marginal product of labor from a production function table. Marginal product (MP) is the additional output produced by one more unit of labor, calculated as the change in total product divided by the change in labor. For the 5th worker, MP = (TP at L=5 - TP at L=4)/(5-4) = (19-16)/1 = 3 yards/day. The 5th worker adds exactly 3 yards to daily production. A common error is reporting total product (19) or average product (19/5=3.8) instead of marginal product. To find any worker's marginal product, subtract the previous total product from the current total product—this gives the additional output that specific worker contributes to production.

3

A delivery service completes deliveries per shift using labor (drivers) as the variable input; the number of vans is fixed. Based on the production data shown in the table, over which range of labor does the firm experience diminishing marginal returns?

Labor (L)Total Product (TP), deliveries/shift
00
19
220
332
443
552
658
761
Question graphic

From $L=2$ to $L=5$ only

From $L=0$ to $L=2$ only

From $L=1$ to $L=7$ (constant marginal returns)

From $L=1$ to $L=4$ only

From $L=4$ to $L=7$

Explanation

This question tests your understanding of diminishing marginal returns in the production function. Marginal product of labor (MPL) is the additional output from each driver, and diminishing returns occur when MPL decreases as labor increases. Calculate MPL: L=1: 9, L=2: 11, L=3: 12, L=4: 11, L=5: 9, L=6: 6, L=7: 3. MPL increases from L=1 to L=3 (9→11→12), then decreases from L=4 to L=7 (11→9→6→3), indicating diminishing returns begin after the 3rd driver. The pattern shows initial gains from specialization followed by congestion effects. To identify diminishing returns, compute MP = ΔTP/ΔL for each worker and find where MP starts declining—this reveals when additional workers contribute less due to fixed van capacity.

4

A coffee shop produces cups of coffee per hour using labor (baristas) as the variable input; espresso machines are fixed. Based on the production data shown in the table, which range shows negative marginal returns to labor?

Labor (L)Total Product (TP), cups/hour
00
112
226
339
449
556
654
Question graphic

From $L=2$ to $L=3$

From $L=5$ to $L=6$

From $L=1$ to $L=2$

From $L=3$ to $L=4$

From $L=4$ to $L=5$

Explanation

This question tests your understanding of negative marginal returns in the production function. Marginal product of labor (MPL) is the additional output from hiring one more worker, and negative marginal returns occur when MPL becomes negative—meaning total product actually decreases when adding labor. Calculate MPL for each worker: L=1: 12, L=2: 14, L=3: 13, L=4: 10, L=5: 7, L=6: -2. From L=5 to L=6, total product falls from 56 to 54, giving MPL = -2 cups/hour. This happens when workers become so crowded they interfere with each other's productivity. Don't confuse diminishing returns (positive but declining MP) with negative returns (negative MP). To identify negative returns, look for where total product decreases as labor increases—this is the only range where hiring more workers actually reduces output.

5

A small greenhouse produces potted plants (single output) using labor as the variable input; the greenhouse space and watering system (capital) are fixed. Based on the production data shown, what is the marginal product of the 7th worker?

Table: Total Product (TP) of Potted Plants

Labor (L), workersTotal Product (TP), plants/day
00
14
29
315
420
524
627
729
828

1 plant per day

3 plants per day

5 plants per day

29 plants per day

2 plants per day

Explanation

This question focuses on the production function and the concept of marginal product of labor in AP Microeconomics. Marginal product (MP) is the additional output from hiring one more worker, and diminishing marginal returns refer to the stage where each additional worker adds less output than the previous one due to fixed capital. Using the provided table, we calculate MP for each worker to understand the pattern. The marginal product of the 7th worker is 29 - 27 = 2 plants per day, as shown by the change in TP from 6 to 7 workers. Don't confuse marginal product with average product, which is TP divided by labor (e.g., AP at 7 workers is 29/7 ≈4.14). To compute marginal product, always use the formula MP = ΔTP / ΔL, where ΔL is usually 1. Look for diminishing returns by observing when MP starts declining as labor increases while capital is fixed.

6

A small app-testing firm completes tested modules per day using labor (testers) as the variable input; computer lab capacity is fixed. Based on the production data shown in the table, over which range of labor does the firm experience diminishing marginal returns?

Labor (L)Total Product (TP), modules/day
00
14
29
315
420
524
627
Question graphic

From $L=1$ to $L=6$ (constant marginal returns)

From $L=3$ to $L=6$

From $L=4$ to $L=6$ only

From $L=1$ to $L=3$ only

From $L=0$ to $L=2$ only

Explanation

This question tests your understanding of diminishing marginal returns in the production function. Marginal product of labor (MPL) is the additional output from each worker, and diminishing returns occur when MPL decreases as labor increases. Calculate MPL for each worker: L=1: 4, L=2: 5, L=3: 6, L=4: 5, L=5: 4, L=6: 3. MPL increases from L=1 to L=3 (4→5→6), then decreases from L=3 to L=6 (6→5→4→3), so diminishing returns begin after the 3rd tester. The key is recognizing that MPL peaks at L=3 then declines. Don't mistake steady total product growth for constant marginal returns—TP can increase while MP decreases. To identify diminishing returns, always calculate MP = ΔTP/ΔL and look for where MP starts declining, indicating reduced productivity gains from additional workers.

7

A farm stand packs boxes of produce per hour using labor (packers) as the variable input; packing tables are fixed. Based on the production data shown in the table, what is the marginal product of the 6th packer?

Labor (L)Total Product (TP), boxes/hour
00
16
213
321
428
534
639
743
Question graphic

$5$ boxes/hour

$6$ boxes/hour

$39$ boxes/hour

$4$ boxes/hour

$6.5$ boxes/hour per packer (average product)

Explanation

This question tests your ability to calculate the marginal product of labor from a production function table. Marginal product (MP) is the additional output produced by one more worker, calculated as the change in total product. For the 6th packer, MP = (TP at L=6 - TP at L=5)/(6-5) = (39-34)/1 = 5 boxes/hour. The 6th packer adds 5 boxes per hour to production. A common error is confusing marginal product with average product (39/6=6.5)—marginal product focuses on the contribution of the specific worker, not the average across all workers. To find any worker's marginal product, use MP = ΔTP/ΔL, subtracting the previous total from the current total to isolate that worker's individual contribution to output.

8

A printing shop produces flyers per hour using labor (workers) as the variable input; printing presses are fixed. Based on the production data shown in the table, over which range of labor does the firm experience diminishing marginal returns?

Labor (L)Total Product (TP), flyers/hour
00
120
245
375
4100
5120
6135
Question graphic

From $L=1$ to $L=6$ (constant marginal returns)

From $L=1$ to $L=4$ only

From $L=2$ to $L=5$ only

From $L=0$ to $L=3$

From $L=4$ to $L=6$

Explanation

This question tests your understanding of diminishing marginal returns in the production function. Marginal product of labor (MPL) is the additional output from each worker, and diminishing returns occur when MPL decreases as more labor is added. Calculate MPL: L=1: 20, L=2: 25, L=3: 30, L=4: 25, L=5: 20, L=6: 15. MPL increases from L=1 to L=3 (20→25→30), then decreases from L=4 to L=6 (25→20→15), indicating diminishing returns begin after the 3rd worker. Don't confuse this with negative returns—total product still increases, just at a decreasing rate. To identify diminishing returns, compute MP = ΔTP/ΔL for each worker and find where MP starts declining, which shows that each additional worker contributes less than the previous one due to fixed capital constraints.

9

A small factory assembles toy robots per hour using labor (assemblers) as the variable input; machinery is fixed. Based on the production data shown in the table, which range shows increasing marginal returns to labor?

Labor (L)Total Product (TP), robots/hour
00
16
214
324
433
540
Question graphic

From $L=2$ to $L=4$

From $L=1$ to $L=5$ (constant marginal returns)

From $L=1$ to $L=3$

From $L=3$ to $L=5$

From $L=4$ to $L=5$ only

Explanation

This question tests your understanding of increasing marginal returns in the production function. Marginal product of labor (MPL) is the additional output from each worker, and increasing returns occur when MPL rises as more labor is added. Calculate MPL: L=1: 6, L=2: 8, L=3: 10, L=4: 9, L=5: 7. MPL increases from L=1 to L=3 (6→8→10), then decreases from L=3 to L=5 (10→9→7). Therefore, increasing marginal returns occur from L=1 to L=3, where each additional assembler contributes more output than the previous one. Don't confuse increasing total product with increasing marginal product—MP must be rising, not just positive. To identify increasing returns, compute MP = ΔTP/ΔL and look for ranges where MP is rising, indicating improved productivity as workers specialize and collaborate effectively.

10

A meal-prep business produces packaged meals (single output) using labor as the variable input; its kitchen equipment (capital) is fixed. Based on the production data shown, what is the marginal product of the 3rd worker?

Table: Total Product (TP) of Packaged Meals

Labor (L), workersTotal Product (TP), meals/hour
00
19
220
332
443
552

20 meals per hour

11 meals per hour

12 meals per hour

9 meals per hour

32 meals per hour

Explanation

This question focuses on the production function and the concept of marginal product of labor in AP Microeconomics. Marginal product (MP) is the additional output from hiring one more worker, and diminishing marginal returns refer to the stage where each additional worker adds less output than the previous one due to fixed capital. Using the provided table, we calculate MP for each worker to understand the pattern. The marginal product of the 3rd worker is 32 - 20 = 12 meals per hour, as shown by the change in TP from 2 to 3 workers. Don't confuse marginal product with average product, which is TP divided by labor (e.g., AP at 3 workers is 32/3 ≈10.67). To compute marginal product, always use the formula MP = ΔTP / ΔL, where ΔL is usually 1. Look for diminishing returns by observing when MP starts declining as labor increases while capital is fixed.

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