Assume that this industry is characterized by perfect competition in both the input and the output markèts: that is, all firms in the digital camera industry are price-takers both in the factor (labor and capital) and product (digital camera) markets. Assume that capital is paid a constant price of $\$ 80$ per unit. Suppose that in the long-run equilibrium the market price of a digital camera is $\$ 10$. Assume that all firms in this industry are identical and face the same cost curves. Fill in the blanks in the following table. \begin{tabular}{|r|r|c|c|c|} \hline $\mathrm{L}$ & $\mathrm{K}$ & $\mathrm{Q}$ & MPL & VMPL \\ \hline 0 & 1 & 0 & $\ldots$ & - \\ \hline 1 & 1 & 1 & (a) & \\ \hline 2 & 1 & 5 & 4 & \\ \hline 3 & 1 & 15 & & (b) \\ \hline 4 & 1 & 20 & & \\ \hline 5 & 1 & 23 & & I \\ \hline 6 & 1 & 24 & & \\ \hline \end{tabular} Note: $L$ is labor; $K$ is capital; $Q$ is output; $T R$ is Total Revenue. $\mathrm{MPL}=\Delta \mathrm{Q} / \Delta \mathrm{L}=$ Marginal Product of Labor, i.e., the additional output generated by employing one more unit of labor. VMPL(or MRP Marginal Revenue Product) $=\Delta T R / \Delta L=(\Delta T R / \Delta Q) \times(\Delta Q / \Delta L)=M R \times M P L=$ value of the marginal product of labor, i.e., the value of the additional output generated by employing one more unit of labor.
Solution
Step 1 ：The Marginal Product of Labor (MPL) is calculated by taking the change in output (ΔQ) divided by the change in labor (ΔL). The Value of the Marginal Product of Labor (VMPL) is calculated by multiplying the MPL by the price of the product. Let's fill in the blanks: (a) The MPL from L=0 to L=1 is (1-0)/(1-0) = 1. (b) The VMPL from L=2 to L=3 is (15-5)*$10/(3-2) = $100. The table filled in: \begin{tabular}{|r|r|c|c|c|} \hline $\mathrm{L}$ & $\mathrm{K}$ & $\mathrm{Q}$ & MPL & VMPL \\ \hline 0 & 1 & 0 & - & - \\ \hline 1 & 1 & 1 & 1 & $10 \\ \hline 2 & 1 & 5 & 4 & $40 \\ \hline 3 & 1 & 15 & 10 & $100 \\ \hline 4 & 1 & 20 & 5 & $50 \\ \hline 5 & 1 & 23 & 3 & $30 \\ \hline 6 & 1 & 24 & 1 & $10 \\ \hline \end{tabular} Note: The MPL decreases as more labor is added, which is consistent with the law of diminishing marginal returns. The VMPL also decreases as more labor is added, indicating that the value of the additional output generated by each additional unit of labor is decreasing.
