Scenario: Victoria Corp. makes running shoes by employing a robotics technology that requires at most a few, but highly skilled, workers for monitoring and maintenance of the robots. Each robot costs $240,000. The table below shows the marginal product of capital (MPK) per month when the firm employs one worker versus when it employs two workers. Each pair of Victoria shoes sells for $150.

-Refer to the scenario above.If the firm decides to employ one worker,and the wage is $40,000 per month,the firm's maximum profit is ________.

Question

Scenario: Victoria Corp. makes running shoes by employing a robotics technology that requires at most a few, but highly skilled, workers for monitoring and maintenance of the robots. Each robot costs $240,000. The table below shows the marginal product of capital (MPK) per month when the firm employs one worker versus when it employs two workers. Each pair of Victoria shoes sells for $150.
 
-Refer to the scenario above.If the firm decides to employ one worker,and the wage is $40,000 per month,the firm's maximum profit is ________.

Quizplus · Accepted Answer

The firm's profit is given by:
Profit = Total Revenue - Total Cost
Total Revenue = Price per unit x Quantity
Quantity is given by the equation:
Q = min(L, K/240,000)
where L is labor input and K is the number of robots.
Let's first consider the case where the firm employs only one worker. From the table, we see that the marginal product of capital (MPK) when employing one worker is 4. So, the firm's production function is:
Q = min(1, K/240,000)
To maximize profit, the firm should produce where marginal cost (MC) equals marginal revenue (MR). The firm's marginal cost is the wage rate divided by the marginal product of labor (MPL), which is:
MC = 40,000/MPK
In this case, since the firm is only employing one worker, MPL equals MPK. So, the firm's marginal cost is:
MC = 40,000/4 = 10,000
The marginal revenue (MR) is simply the price per unit, which is $150. Therefore, we have:
MC = MR
10,000 = 150
So, the firm should not produce in this case, since the cost of producing one unit exceeds the revenue generated from selling that unit. The firm's maximum profit in this case is 0.

Now let's consider the case where the firm employs two workers. From the table, we see that the MPK when employing two workers is 3. So, the firm's production function is:
Q = min(2, K/240,000)
To maximize profit, the firm should produce where marginal cost (MC) equals marginal revenue (MR). The firm's total cost in this case consists of the cost of the robots and the two workers' wages. The cost of the robots is simply the number of robots multiplied by their cost ($240,000), which is:
240,000 x K
The cost of labor is simply the sum of the two workers' wages, which is:
2 x 40,000 = 80,000
So, the firm's total cost is:
TC = 240,000K + 80,000
The firm's marginal cost is the derivative of total cost with respect to quantity, which is:
MC = 240,000 x (dK/dQ)
Using the production function above, we can find dK/dQ as follows:
If Q = 2, then dK/dQ = 240,000
If Q = K/240,000, then dK/dQ = 240,000/2 = 120,000
Therefore, the firm's marginal cost when producing two units is:
MC = 240,000 x (dK/dQ) = 240,000 x 120,000 = 28,800,000
The marginal revenue (MR) is simply the price per unit, which is $150. Therefore, we have:
MC = MR
28,800,000 = 150 x 2
28,800,000 = 300
So, the firm should not produce in this case either, since the cost of producing two units exceeds the revenue generated from selling those units. The firm's maximum profit in this case is 0.

Therefore, the best choice is not to produce, as the firm would not make any profit if it employs one or two workers.