Exam 6: Inputs and Production Functions

The marginal rate of technical substitution in production is analogous to the marginal rate of substitution for the consumer's optimization problem in that they are calculated by subtracting the price ratio from the output level.

Consider comparing the relationship between marginal and average product. When average product is decreasing in labor, marginal product is less than average product. That is, if $\mathrm { AP } _ { \mathrm { L } }$ decreases in $\mathrm { L }$ , then $\mathrm { MP } _ { \mathrm { L } } < \mathrm { AP } _ { \mathrm { L } }$ .

Consider the production function $Q = \left[ c + a L ^ { \frac { \sigma - 1 } { \sigma } } + b K ^ { \frac { \sigma - 1 } { \sigma } } \right] ^ { \frac { \sigma } { \sigma - 1 } }$ where $c$ is some constant different than zero. This production function exhibits:

Let a firm's production function be The production function then becomes Capital-saving technological progress has occurred.

A labor requirements function represents:

0 0 1 20 2 50 3 90 4 125 5 140 6 150 -Given the table above, average productivity is maximized with the ____________ worker.

Consider a production function of the form $Q = K ^ { 2 } L ^ { 2 }$ with marginal products $\mathrm { MP } _ { \mathrm { K } } = 2 \mathrm { KL } ^ { 2 }$ and $\mathrm { MP } _ { \mathrm { L } } = 2 \mathrm {~K} ^ { 2 } \mathrm {~L}$ . What is the marginal rate of technical substitution of labor for capital at the point where $\mathrm { K } = 5$ and $\mathrm { L } = 5$ ?

For a simple graph of a production function with Q on the y-axis and L on the x-axis, which of the following statements is true?

The law of diminishing marginal returns states that as the use of one input increases holding the quantities of the other inputs fixed, the marginal product of the input eventually declines.

For the production function $Q = a K + b L$ , where the variables are graphed as usual, the equation for a typical isoquant is $K = a Q - b L$ .

Technically inefficient points only exist with older firms.

When a production function has the form $\mathrm { Q } = \mathrm { aL } + \mathrm { bK }$ , we can say that:

The marginal rate of technical substitution in production is analogous to the marginal rate of substitution for the consumer's optimization problem in that the slope of the consumer's indifference curve is equal to the ratio of the marginal utilities of the two goods, whereas the slope of the production isoquant is the opposite of the ratio of the marginal product of labor relative to the marginal product of capital.

The law of diminishing marginal returns states that when the marginal product is above the average product, average product must be increasing.

Returns to scale pertains to the impact on output of increasing all inputs simultaneously; diminishing marginal returns pertains to the impact of changing a single input while holding all other inputs constant.

Let a firm's production function be $Q = 100 ( a L + b K )$ . The production function then becomes $Q = 500 ( a L + b K )$ . Economies of scale have increased.

When a production function can be expressed as $Q = ( a K ) ( b L )$ the relationship between capital and labor in the production function is that:

Let a firm's production function be $Q = 100 ( a L + b K )$ . The production function then becomes $Q = 500 ( a L + b K )$ . Neutral technological progress has occurred.

The labor requirements function is derived from: