Question

Suppose that low-skilled workers employed in clearing woodland can each clear one acre per month if each is equipped with a shovel, a machete, and a chainsaw. Clearing one acre brings in $$\$ 1,000$$ in revenue. Each worker's equipment costs the worker's employer $$\$ 150$$ per month to rent and each worker toils 40 hours per week for four weeks each month. LO17.6 a. What is the marginal revenue product of hiring one lowskilled worker to clear woodland for one month? b. How much revenue per hour does each worker bring in? c. If the minimum wage were $$\$ 6.20$$, would the revenue per hour in part \(b\) exceed the minimum wage? If so, by how much per hour? d. Now consider the employer's total costs. These include the equipment costs as well as a normal profit of $$\$ 50$$ per acre. If the firm pays workers the minimum wage of $$\$ 6.20$$ per hour, what will the firm's economic profit or loss be per acre? e. At what value would the minimum wage have to be set so that the firm would make zero economic profit from employing an additional low-skilled worker to clear woodland?

Short answer

a. $1,000; b. $6.25; c. Yes, by $0.05; d. Loss of $192; e. Minimum wage must be $5.

Step-by-step solution

Calculate the Marginal Revenue Product

The marginal revenue product (MRP) of a worker is the additional revenue the company earns from hiring one more worker. Here, a worker clears one acre per month, generating $1,000 in revenue. Thus, MRP = $1,000 per month.

Determine Revenue Per Hour Brought in by Worker

Each worker works 40 hours per week for 4 weeks, totaling 160 hours a month. To find revenue per hour, divide the total revenue per month by the total hours worked:\[\text{Revenue per hour} = \frac{1000}{160} = 6.25\] Thus, a worker brings in $6.25 per hour.

Compare to Minimum Wage

The minimum wage is \(6.20 per hour. Compare the revenue per hour to the minimum wage:Revenue per hour: \)6.25Since \(6.25 > \)6.20, the revenue exceeds the minimum wage by:\[6.25 - 6.20 = 0.05\] Thus, the revenue exceeds the minimum wage by $0.05 per hour.

Compute Economic Profit or Loss Per Acre at Minimum Wage

First, calculate the total wage cost per worker:\[ \text{Wage cost} = 160 \times 6.20 = 992 \]Add equipment cost of \(150 and normal profit of \)50 per acre:Total cost per acre = \(992 (wage) + \)150 (equipment) + \(50 (normal profit) = \)1,192.Economic profit (or loss) per acre: Revenue - Total costProfit/loss = \(1,000 - \)1,192 = -\(192.The firm incurs a loss of \)192 per acre.

Calculate Minimum Wage for Zero Economic Profit

To find the wage that results in zero economic profit, set profit/loss to zero:Let the new wage per hour be \(w\).\[ 160w + 150 + 50 = 1000 \]\[ 160w = 800 \]\[ w = \frac{800}{160} = 5 \]So, the minimum wage must be $5 per hour for zero economic profit.

Key concepts

Economic Profit

Economic profit differs from regular accounting profit. While accounting profit simply measures total revenue minus total costs, economic profit takes into account opportunity costs as well. In other words, economic profit reflects both explicit costs (actual money spent) and implicit costs (the value of foregone opportunities).

To illustrate, imagine you run a business and have a choice between paying your workers a minimum wage and spending on equipment. You also have to consider the normal profit, which is the minimum return necessary to keep you in business in this sector, which in this case is given as $50 per acre. Thus, if your total costs, including wages and equipment, exceed the revenue you generate, you'll suffer an economic loss. In this scenario, the revenue from clearing land ($1,000) does not cover the total costs of $1,192, leading to a loss of $192 per acre. This loss represents the firm's economic profit, which is indeed negative in this instance.

Minimum Wage

Minimum wage refers to the lowest hourly pay that workers are legally guaranteed. It's a critical aspect of labor economics as it ensures basic earnings for employees. In our case, the minimum wage is set at $6.20 per hour. Here's why it's important:

• Ensures a basic standard of living for low-skilled workers.
• Affects an employer’s cost structure and pricing ability.
• Determines the economic viability of hiring additional workers.

In this exercise, we observe that the revenue each worker generates per hour ($6.25) is slightly above the minimum wage. Thus, while the worker covers their wages, they don’t cover the full cost (including equipment and normal profit) required by the employer, leading to an economic loss. Moreover, for the firm to achieve zero economic profit, the minimum wage would need to be reduced to $5 per hour. This would align costs with revenue, ensuring the firm's sustainability without incurring a loss.

Revenue per Hour

Calculating revenue per hour is essential for understanding workers' contribution to a company’s income. It involves dividing total revenue generated by the total hours worked. Here’s how it was computed in this scenario:

- Each worker generates \(1,000 by clearing one acre in a month.- They work 160 hours per month (calculated as 40 hours per week for 4 weeks).
Thus, the revenue per hour is calculated as:
\[\text{Revenue per hour} = \frac{1000}{160} = 6.25\]
This implies that for each hour worked, the company gains \)6.25. Since this figure slightly surpasses the minimum wage of $6.20, it articulates how each worker's hourly productivity affects both their worth to an employer and impacts employment and wage-setting strategies. Ensuring that revenue per hour is greater than wage per hour is crucial for sustainable employment.