Question

Consider a firm with the production function Q= √KL

, where K is amount of capital and L is amount of labor. a) Write down the equation of the isoquant corresponding to Q=20. Provide the plot of the isoquant, putting K on y-axis and L on x-axis. b) Write down the general equation of the isoquant corresponding to any level of output Q. c) Find the technical rate of substitution (of labor for capital) when the firm produces 20 units of output with 40 units of labor and the corresponding amount of capital.

Answer 1

The isoquant corresponding to Q=20 can be described by K=(Q^2)/L. The general equation of the isoquant is K=(Q^2)/L. The technical rate of substitution when producing 20 units of output with 40 units of labor is -1.

Step-by-step explanation:

The isoquant representing Q=20, given by the equation K=(Q^2)/L, indicates the combinations of capital (K) and labor (L) that yield a constant level of output (Q=20). The general isoquant equation K=(Q^2)/L emphasizes the inverse relationship between capital and labor inputs to maintain the same level of output.

To calculate the technical rate of substitution (TRS) when producing 20 units of output with 40 units of labor, the TRS is determined by the negative of the marginal rate of technical substitution (MRTS). The MRTS represents the rate at which one input can be reduced while increasing the other input to keep output constant. In this case, with the isoquant equation, the MRTS is -1, indicating that for each unit decrease in labor (L), one unit increase in capital (K) is required to maintain the production of 20 units of output. The negative sign signifies the inverse relationship between capital and labor inputs.