Question 1

The marginal rate of technical) substitution is equal to the inverse of the slope of an isoquant.

Accepted Answer

The marginal rate of technical substitution (MRTS) is equal to the negative of the slope of an isoquant, not the inverse. It represents the rate at which one input can be substituted for another while keeping output constant.

Question 2

A least-cost combination of inputs requires that the marginal product per dollar spent on each variable input be equal.

Accepted Answer

A least-cost combination of inputs is obtained when the marginal product per dollar spent on each variable input is equal. This is known as the principle of equal marginal productivity. By allocating spending across inputs in such a way that the marginal product per dollar is equal, firms can minimize their costs while producing a given level of output.

Question 3

The marginal product of a variable input is the rate of change of total product with respect to the input, all other things kept fixed.

Accepted Answer

The definition of marginal product is correct.

Question 4

The short run is a period so brief that the amount of at least one input, or factor of production, is fixed.

Accepted Answer

In the short run, at least one input is fixed, meaning it cannot be adjusted to changes in output. This is different from the long run, where all inputs can be adjusted.

Question 5

With output held constant, for a combination of inputs to be a least cost combination, the slopes of an isocost line and the isoquant curve must be equal at the point the where the two curves touch.

Accepted Answer

This is true according to the concept of marginal rate of technical substitution (MRTS). At the point where the two curves touch, the MRTS equals the ratio of input prices, which is the slope of the isocost line. Therefore, for the combination of inputs to be a least cost combination, the slope of the isoquant must also be equal to the ratio of input prices, which is the slope of the isocost line.

Question 6

For each possible combination of inputs, the production function indicates the minimum quantity of output that can be produced.

Accepted Answer

The production function indicates the maximum quantity of output that can be produced for a given set of inputs, not the minimum quantity.

Question 7

A production function is a mathematical statement of the way that the quantity of output of a particular product depends on the use of specific inputs, or resources.

Accepted Answer

This is a definition of a production function.

Question 8

The long run is a period of time long enough for at least one input, or factor of production, to vary as far as the individual firm is concerned.

Accepted Answer

In the long run, all factors of production are variable, allowing firms to adjust all inputs and production levels.

Question 9

The long run is a period of time long enough for all inputs, or factors of production, to be variable as far as the individual firm is concerned.

Accepted Answer

In the long run, all inputs are variable for the firm, meaning they can adjust their level of capital, labor, raw materials, etc. Therefore, the long run is a period of time long enough for all factors of production to be variable.

Question 10

At the point where MP_L is equal to zero, TP_L is at its maximum.

Accepted Answer

This is because MPS (mean path to satisfaction) and TPS (total path to satisfaction) are inversely related. When one reaches its minimum, the other reaches its maximum. So, when MP_L (which represents the minimum mean path to satisfaction) is equal to zero, TP_L (which represents the maximum total path to satisfaction) is at its highest point.

Question 11

The marginal product of a variable input is the rate of change of average product with respect to the input, all other things kept fixed.

Accepted Answer

The marginal product of a variable input is the additional output produced by adding one more unit of that input, while holding all other inputs constant. It is not related to the rate of change of average product.

Question 12

An isoquant is a contour line that shows the various combinations of two inputs that will produce a given level of output.

Accepted Answer

This is the correct definition of an isoquant.

Question 13

The reason that we can say that the production function indicates the maximum quantities that can be produced with each combination of inputs is because we are assuming that all of the inputs are being used efficiently.

Accepted Answer

The production function assumes that all inputs are being used efficiently, therefore indicating the maximum quantities that can be produced with each combination of inputs.

Question 14

The short run is a period so brief that the amount of at least one input, or factor of production, is variable.

Accepted Answer

In the short run, at least one input or factor of production is fixed, not variable.

Question 15

Fat Cat Farms Inc. is a small catfish farm. Fat Cat estimates that output would increase by 1800 pounds per month with an additional 2,000 pounds of catfish food provided monthly by a new feeding system. Alternatively, output could be increased by 3,000 pounds per month with an additional 20,000 gallons of fresh water per month. Assuming the cost of water is $.06 per gallon and that fertilizer is $.25 per pound, Fat Cat is using an optimal combination of fish food and water.

Accepted Answer

To determine the optimal combination of fish food and water, we need to compare the Marginal Physical Product (MPP) and Marginal Cost (MC) of each input. Without information about the MC of each input, we cannot confidently determine whether Fat Cat is using an optimal combination.

Question 16

For each possible combination of inputs, the production function indicates the maximum quantity of output that can be produced.

Accepted Answer

The production function is a mathematical representation of the relationship between inputs and outputs and specifies the maximum quantity of output that can be produced for each combination of inputs.

Question 17

An isocost curve is a line that represents all combinations of inputs that can be employed for a given cost.

Accepted Answer

This is the definition of an isocost curve.

Question 18

The expansion path of a firm refers to the path that connects least cost combinations of input for different levels of output, assuming constant input prices.

Accepted Answer

This definition accurately reflects the concept of an expansion path.

Question 19

Hill Country Farms Inc. is a small grower of peaches. Hill Country estimates that peach output would increase by 600 bushels per season with an additional 6,000 gallons of water provided strategically throughout the season by an existing irrigation system. Alternatively, peach output could be increased by 500 bushels per season with an additional 2 tons of fertilizer applied at the beginning of the season. Given the cost of water is $.01 per gallon and that fertilizer is $25 per ton, Hill Country Farms is using an optimal combination of fertilizer and water.

Accepted Answer

To determine the optimal combination of inputs, we need to calculate the marginal product per dollar of each input. For water, the marginal product per dollar is 60 (600 bushels / 6,000 gallons * $0.01 per gallon). For fertilizer, the marginal product per dollar is 20 (500 bushels / 2 tons * $25 per ton). The marginal product per dollar of water is higher than that of fertilizer, indicating that Hill Country Farms should use more water and less fertilizer to maximize profits. Therefore, the current combination of inputs is optimal.

Question 20

The marginal rate of technical) substitution is equal to the negative of the slope of the isoquant and shows how much of one input can be substituted for another, output constant.

Accepted Answer

This is a correct definition of the marginal rate of technical substitution.

Quiz 5: Production Analysis