Question\begin{tabular}{|c|c|c|c|c|}
\hline Labor Demand Data & Labor Supply Data & \multicolumn{3}{|c|}{,} \\
\hline Employment & Toatal Product & Product Price & Employment & Wage Rate \\
\hline 0 & 0 & \$2.20 & 0 & - \\
\hline 1 & 15 & 2.00 & 1 & \$1.00 \\
\hline 2 & 28 & 1.80 & 2 & 2.00 \\
\hline 3 & 39 & . 1.60 & 3 & 3.00 \\
\hline 4 & 48 & 1.40 & 4 & 4.00 \\
\hline 5 & 55 & 1.20 & 5 & 5.00 \\
\hline 6 & 60 & 1.00 & 6 & 6.00 \\
\hline
\end{tabular}
The table shows labor demand data on the left and labor supply data on the right. How many workers will this profit-maximizing firm choose to employ?
(A) 5
(B) 3
(C) 4
(D) 6
Studdy Solution
STEP 1
1. The firm aims to maximize profit.
2. Profit maximization occurs where marginal revenue product (MRP) equals marginal cost (MC), which is the wage rate.
3. MRP is calculated as the change in total product multiplied by the product price.
STEP 2
1. Calculate the Marginal Revenue Product (MRP) for each level of employment.
2. Compare MRP to the wage rate to determine the profit-maximizing level of employment.
STEP 3
Calculate the MRP for each level of employment. MRP is the change in total product times the product price.
\begin{align*}
\text{MRP}_1 & = (15 - 0) \times 2.00 = 30.00 \\
\text{MRP}_2 & = (28 - 15) \times 1.80 = 23.40 \\
\text{MRP}_3 & = (39 - 28) \times 1.60 = 17.60 \\
\text{MRP}_4 & = (48 - 39) \times 1.40 = 12.60 \\
\text{MRP}_5 & = (55 - 48) \times 1.20 = 8.40 \\
\text{MRP}_6 & = (60 - 55) \times 1.00 = 5.00 \\
\end{align*}
STEP 4
Compare MRP to the wage rate for each level of employment to find where MRP equals or is just above the wage rate.
\begin{align*}
\text{Wage Rate}_1 & = 1.00, \quad \text{MRP}_1 = 30.00 \\
\text{Wage Rate}_2 & = 2.00, \quad \text{MRP}_2 = 23.40 \\
\text{Wage Rate}_3 & = 3.00, \quad \text{MRP}_3 = 17.60 \\
\text{Wage Rate}_4 & = 4.00, \quad \text{MRP}_4 = 12.60 \\
\text{Wage Rate}_5 & = 5.00, \quad \text{MRP}_5 = 8.40 \\
\text{Wage Rate}_6 & = 6.00, \quad \text{MRP}_6 = 5.00 \\
\end{align*}
The firm will employ up to the point where MRP is just greater than or equal to the wage rate. This occurs at:
The profit-maximizing number of workers to employ is:
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