Suppose the production function for a firm is given by: q=4L +2K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSLK).(Round to the nearest two decimal places if necessary.)

Question

BlackTom AI · Accepted Answer

We start by identifying the marginal products from the given production function q = 4L + 2K.

- The marginal product of labor (MPL) is the partial derivative of q with respect to L: MPL = ∂q/∂L = 4. 
- The marginal product of capital (MPK) is the partial derivative of q with respect to K: MPK = ∂q/∂K = 2.

The marginal rate of technical substitution of labor for capital (MRTSLK) is the rate at which capital can be substituted for labor while holding output constant, which in this linear production setup equals the ratio of MPL to MPK: MRTSLK = MPL / MPK.

Plugging in the values, MRTSLK = 4 / 2.

Thus, the calculation involves computing the two marginal products and forming their ratio, showing how much K could be traded for an additional unit of L along an isoquant given the production function structure.

Suppose the production function for a firm is given by: q=4L +2K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSLK).(Round to the nearest two decimal places if necessary.)

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