Question at position 3 The wage rate is $10 per hour and the last worker hired by the firm increased output by 100 units. Computers rent for $100 per hour and the last computer rented by the firm increased output by 2,000 units. To minimize costs the firm should keep the same number of workers and computers because the marginal revenue products of both workers and computers are positivehire more workers and reduce the number of computers rented because workers are cheaper than computershire more workers and rent more computers because the marginal revenue products of both workers and computers are greater than their respective prices.lay off workers and rent more computers because computers produce more outputlay off workers and rent more computers because computers produce more output per dollar of additional expenditure.

Question

Question at position 3  The wage rate is $10 per hour and the last worker hired by the firm increased output by 100 units. Computers rent for $100 per hour and the last computer rented by the firm increased output by 2,000 units. To minimize costs the firm should keep the same number of workers and computers because the marginal revenue products of both workers and computers are positivehire more workers and reduce the number of computers rented because workers are cheaper than computershire more workers and rent more computers because the marginal revenue products of both workers and computers are greater than their respective prices.lay off workers and rent more computers because computers produce more outputlay off workers and rent more computers because computers produce more output per dollar of additional expenditure.

BlackTom AI · Accepted Answer

Question: The wage rate is $10 per hour and the last worker hired by the firm increased output by 100 units. Computers rent for $100 per hour and the last computer rented by the firm increased output by 2,000 units. To minimize costs the firm should

Options:
1) keep the same number of workers and computers because the marginal revenue products of both workers and computers are positive
2) hire more workers and reduce the number of computers rented because workers are cheaper than computers
3) hire more workers and rent more computers because the marginal revenue products of both workers and computers are greater than their respective prices.
4) lay off workers and rent more computers because computers produce more output
5) lay off workers and rent more computers because computers produce more output per dollar of additional expenditure.

Analysis of each option:
Option 1: keep the same number of workers and computers because the marginal revenue products of both workers and computers are positive.
- This option asserts that positive marginal revenue products (MRP) imply no change is needed. However, MRP being positive only means the resource contributes net revenue; it does not guarantee that current employment levels minimize costs. If the cost of an input is small relative to the revenue it generates, it may be optimal to hire more; conversely, if an input is less productive per dollar spent than alternatives, laying off could be better. Here, since computers yield more output per dollar than workers, simply keeping both fixed ignores the relative efficiency, so this option is not the cost-minimizing choice.

Option 2: hire more workers and reduce the number of computers rented because workers are cheaper than computers
- This suggests shifting resources toward the cheaper input. But cost-minimization depends on output gained per dollar spent, not just per-hour price. Although workers are cheaper per hour, the worker’s output per dollar is lower than that of the computer (100 units per $10 vs 2000 units per $100). Therefore, reallocating toward more workers would reduce output per dollar and raise cost per unit of output, making this option suboptimal.

Option 3: hire more workers and rent more computers because the marginal revenue products of both workers and computers are greater than their respective prices.
- This option uses a rule that compares MRP to input price: if MRP > price, hire more of that input. While it’s true that MRPs exceed their prices here (since 100p > 10 and 2000p > 100 for any positive price p of the product), the phrase implies you should increase both inputs. However, the stronger efficiency metric is output per dollar spent. Even if both MRPs exceed input costs, we must consider the relative efficiency; since computers yield more output per dollar than workers, the optimal move is to reallocate toward computers rather than expand both or focus on workers. This makes the option incomplete/less precise for cost minimization in this context.

Option 4: lay off workers and rent more computers because computers produce more output
- This states lay off workers and rent more computers, arguing on absolute output differences (computers produce more output overall). But cost-minimization hinges on output per dollar spent, not just total output. Since a computer adds 2000 units for $100 (20 units per dollar) and a worker adds 100 units for $10 (10 units per dollar), computers are more productive per dollar. This option captures the correct directional shift (reduce workers, expand computers) and cites the greater output from computers, but it omits the crucial detail that the decision is about output per dollar, not just total output. It is closer to correct than options 1–3, but still incomplete if interpreted strictly about per-dollar efficiency.

Option 5: lay off workers and rent more computers because computers produce more output per dollar of additional expenditure.
- This option directly uses the cost-minimization logic: compute output per dollar spent for each input. A worker: 100 units for $10 = 10 units per dollar. A computer: 2000 units for $100 = 20 units per dollar. Since computers give more output per dollar, the firm should reduce the cheaper-to-hire input (workers) and increase the more productive-in-per-dollar input (computers). This yields a lower cost per unit of output, aligning with cost-minimization goals. The phrase 'per dollar of additional expenditure' correctly emphasizes efficiency per dollar spent, making this the most precise and economically sound recommendation among the options.

Summary: Among the provided choices, Option 5 best matches the cost-minimization principle by comparing output gains per dollar spent and recommending reallocating toward the input with higher output per dollar (computers) while reducing the use of the less efficient per-dollar input (workers).

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