Question

A more general form of the perfect substitutes production function is ?=??,?=??+??, where ?,?>0.

a.What does this production function tell you about how these inputs are used?

b.Use calculus to solve for the marginal product of labor (MPL).c.Use calculus to solve for the marginal product of capital (MPK)

.d.Using what you found in (b) and (c), solve for the ????LK

e.In one sentence, interpret what the ???LK !tells you if ?=10,?=20and ?=10;?=20

.f.Suppose that ?=10,?=20. Derive an equation for the isoquant ?=100and graph it with labor on the x-axis and capital on the y-axis. Be sure to include at least two ordered pairs on your graph.

Answer 1

a) As it is given in the question that it is a perfect substitutes production function. This means that the two inputs that is labor and capital can be substituted for each other at the constant rate while maintaining the same output level. In a case like this, we often get a corner solution which means that either of the two inputs are fully used and sometimes we get a combination of the two inputs which is used in the production process.

b) Marginal product of labor is calculated by differentiating the production function with respect to labor keeping capital constant.

So, in this case marginal product of labor = a.

c) Marginal product of capital is calculated by differentiating the production function with respect to capital keeping labor constant.

So, in this case marginal product of capital = b.

d) Marginal rate of technical substitution is the rate at which one input is substituted for the other input to produce a given level of output.

Marginal rate of technical substitution = marginal product of labor / marginal product of capital

Marginal rate of technical substitution = a / b is the answer.