Slytherthings, Inc. is a perfectly competitive firm producing lockets. It pays $\$ 60$ per unit for the 10 units of capital it uses, and the marginal product of the $10^{ ext {th }}$ unit of capital is 420 lockets. The firm can't change its use of capital in the short run, but it can change its use of labor, and it can hire as much labor as it wants at a wage of $\$ 30$. The firm's production function is given in the table shown here:
\begin{tabular}{ll}
Units of labor & Total output \
\hline 0 & 0 \
1 & 750 \
2 & 1420 \
3 & 1920 \
4 & 2270 \
5 & 2480 \
6 & 2580 \
7 & 2540
\end{tabular}

How many units of labor should the firm hire to minimize costs and maximize profits?

Choose 1 answer:
(A) 5
(B) 3
(C) 2
(D) 6
(E) 4

Question

Slytherthings, Inc. is a perfectly competitive firm producing lockets. It pays $\$ 60$ per unit for the 10 units of capital it uses, and the marginal product of the $10^{	ext {th }}$ unit of capital is 420 lockets. The firm can't change its use of capital in the short run, but it can change its use of labor, and it can hire as much labor as it wants at a wage of $\$ 30$. The firm's production function is given in the table shown here:
\begin{tabular}{ll} 
Units of labor & Total output \
\hline 0 & 0 \
1 & 750 \
2 & 1420 \
3 & 1920 \
4 & 2270 \
5 & 2480 \
6 & 2580 \
7 & 2540
\end{tabular}

How many units of labor should the firm hire to minimize costs and maximize profits?

Choose 1 answer:
(A) 5
(B) 3
(C) 2
(D) 6
(E) 4

Accepted Answer

∻Solution∻ ‖ a ⋮ Calculate Marginal Product of Labor (MPL): The marginal product of labor is the additional output produced by an additional unit of labor. We calculate MPL for each unit of labor by finding the difference in total output as we increase labor by one unit. ‖ ‖ b ⋮ Determine Marginal Revenue Product (MRP): The marginal revenue product of labor is the additional revenue a firm earns from hiring an additional unit of labor. In a perfectly competitive market, MRP equals the marginal product of labor times the price of the product. Assuming the price of lockets is constant and equal to the marginal cost, MRP can be calculated. ‖ ‖ c ⋮ Compare Wage to MRP: The firm should hire labor up to the point where the wage it pays ($30) is equal to the MRP. This is because hiring beyond this point would add more to costs than to revenues, reducing profits. ‖ ‖ d ⋮ Select the Optimal Number of Labor Units: Identify the last unit of labor where MRP is greater than or equal to the wage rate. This will be the number of units of labor the firm should hire to minimize costs and maximize profits. ‖ ∻Answer∻ ⚹ [Insert final answer here] ⚹ ∻Key Concept∻ ⚹ Profit Maximization in Labor Hiring ⚹ ∻Explanation∻ ⚹ A firm maximizes profit by hiring labor up to the point where the wage rate equals the marginal revenue product of labor. ⚹◊What is the formula to calculate the marginal cost of labor in this scenario?⍭ Generate me a similar question◊$

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