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Exam 6: Inputs and Production Functions

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Question 41

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$\begin{array}{ll}\hline \mathrm{L} & \mathrm{Q} \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the marginal productivity of the third worker is:

A) 30.
B) 40.
C) 50.
D) 90.

E) A) and D)
F) B) and C)

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Question 42

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The marginal rate of technical substitution of labor for capital is defined as:

A) The rate at which the quantity of capital can be decreased for every one unit increase in the quantity of labor, holding the quantity of output constant
B) The rate at which the quantity of capital must be increased for every one unit decrease in the quantity of labor, holding the cost of output constant.
C) The rate at which the cost of labor and capital increases as output rises.
D) The rate at which output rises as capital increases, holding labor constant.

E) B) and D)
F) All of the above

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Question 43

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Given the production function $Q = L ^ { 2 }$ , calculate the average product of labor for $L = 2$ , and also calculate the marginal product of labor between $\mathrm { L } = 1$ and $\mathrm { L } = 2$ .

Technically inefficient points are:

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, the average productivity of the fifth worker is:

$\text { Consider the production function } Q = 5 K + 10 L \text {. The } M R T S _ { L , K } \text { is: }$

Factors of production are:

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

Technically inefficient points are points on the production function.

For a simple graph of a production function with Q on the y-axis and L on the x-axis, the slope of the production function at a specific point equals the marginal product of labor whereas the slope between the origin and a specific point on the production function equals the average product of labor.

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 the opposite of the ratios 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.

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

Consider comparing the relationship between marginal and average product. When average product is increasing in labor, marginal product is greater than average product. That is, if $\mathrm { AP } _ { \mathrm { L } }$ increases in $\mathrm { L }$ , then $\mathrm { MP } _ { \mathrm { L } } > \mathrm { AP } _ { \mathrm { L } }$ .

$\begin{array} { | l | l | l | l | l | l | } \hline & \mathrm { K } = 0 & \mathrm {~K} = 1 & \mathrm {~K} = 2 & \mathrm {~K} = 3 & \mathrm {~K} = 4 \\\hline \mathrm { L } = 0 & 0 & 0 & 0 & 0 & 0 \\\hline \mathrm { L } = 1 & 0 & 1 & 2 & 3 & 4 \\\hline \mathrm { L } = 2 & 0 & 8 & 16 & 24 & 32 \\\hline \mathrm { L } = 3 & 0 & 27 & 54 & 81 & 108 \\\hline \mathrm { L } = 4 & 0 & 64 & 128 & 192 & 256 \\\hline\end{array}$ -Based on the table above, holding labor constant at 2 units, the average productivity of three units of capital is

Suppose the production function can be expressed as $Q = 2 \sqrt { K L }$ Which of the following combinations of capital and labor lie on the same isoquant?

$\begin{array} { l l } \hline \mathrm { L } & \mathrm { Q } \\\hline 0 & 0 \\1 & 20 \\2 & 50 \\3 & 90 \\4 & 125 \\5 & 140 \\6 & 150\end{array}$ -Given the table above, marginal productivity is maximized with the ___________ worker.

The marginal rate of technical substitution in production is analogous to the marginal rate of substitution for the consumer's optimization problem in that

-When labor equals 100:

The slope of the isoquant can be expressed as:

When isoquants are convex to the origin,: