ECO CH. 6

When capital is plotted on the vertical axis and labor is plotted along the horizontal​ axis, the marginal rate of technical substitution​ (MRTS) of labor for capital along a convex isoquant

-equals the negative of the slope of the isoquant. -declines as more and more labor is used. -equals the marginal product of labor divided by the marginal product of capital.

Explain the term​ "marginal rate of technical​ substitution." ​(Assume a​ two-input production function.​)

MRTS is the amount by which the quantity of one input can be reduced when the other input is increased by one​ unit, while maintaining the same level of output.

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or​ low, or is further information​ necessary? Discuss. --- In this​ example, the marginal rate of technical substitution​ (MRTS) is

The MRTS is the absolute value of the slope of an isoquant. If the inputs are perfect​ substitutes, then the isoquants will be linear. To calculate the slope of the​ isoquant, and hence the​ MRTS, we need to know the rate at which one input may be substituted for the other. In this​ instance, we do not know whether the MRTS is high or low. All we know is that it is a constant number. We need to know the marginal product of each input to determine the MRTS. --- Constant but otherwise unknown without information about the marginal product of each input.

What is the long​ run?

An amount of time needed to make all production inputs variable.

Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital.

As the quantities of the inputs are​ changed, the marginal product of each input will change. As more and more labor is​ added, the marginal product of labor is likely to diminish. Because capital has been​ reduced, each unit of capital remaining is likely to be more productive. ​ Therefore, more units of labor will be required to replace each unit of capital. ​ Alternatively, as we move down and to the right along an isoquant along which the MRTS is​ diminishing, we have to give up less capital for each unit of labor added to keep output constant. -- The substitution of labor for capital decreases the MP,L and increases the MP,K. Since the MRTS is the ratio of the former to the​ latter, it will diminish as this substitution occurs.

If you observe that your average product is just beginning to​ decline, should you hire any more​ workers? What does this situation imply about the marginal product of your last worker​ hired?

At the point where average product begins to​ decline, marginal product is equal to average product. Since total product continues to​ increase, it may still be advantageous to hire another worker.

The production function q=L/2 is associated with

Constant returns to scale. --- Let q' be output when labor is doubled to 2L. Then q'=2L/2=L. Compare q' to q by dividing q' by q. This gives us q'q=L/L/2=2. ​Therefore, when the amount of labor is​ doubled, output is also doubled. ​ Hence, there are constant returns to scale.

Which of the following is an example of the law of diminishing marginal​ returns?

Holding capital​ constant, when the amount of labor increases from 5 to​ 6, output increases from 20 to 25. Then when labor increases from 6 to​ 7, output increases from 25 to 28.

You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average product of labor or the marginal product of labor for the last person​ hired?

In filling a vacant​ position, you should be concerned with the marginal product of the last worker hired because the marginal product measures the effect on​ output, or total​ product, of hiring another worker. This in turn will help to determine the revenue generated by hiring another​ worker, which can then be compared to the cost of hiring that worker. OK

L-shaped isoquant

The inputs are perfect​ complements, or that the firm is producing under a fixed proportions type of technology. In this​ case, the firm cannot give up one input in exchange for the other and still maintain the same level of output.

Do the following functions exhibit​ increasing, constant, or decreasing returns to​ scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor is held​ constant? q=(2L+2K)^1/2

The production function exhibits decreasing returns to scale. The marginal product of labor is decreasing and the marginal product of capital is decreasing

Do the following functions exhibit​ increasing, constant, or decreasing returns to​ scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor is held​ constant? q=L^1/2*K^1/2

The production function exhibits constant returns to scale. The marginal product of labor is decreasing and the marginal product of capital is decreasing

Do the following functions exhibit​ increasing, constant, or decreasing returns to​ scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor is held​ constant? q=4L^1/2+4K

The production function exhibits decreasing returns to scale. The marginal product of labor is decreasing and the marginal product of capital is constant

Do the following functions exhibit​ increasing, constant, or decreasing returns to​ scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor is held​ constant? q=3LK^2

The production function exhibits increasing returns to scale. The marginal product of labor is constant and the marginal product of capital is increasing

Linear isoquant

The​ slope, or the​ MRTS, is constant. This means that the same number of units of one input can always be exchanged for a unit of the other input and output can be maintained. The inputs are perfect substitutes.

Do the following functions exhibit​ increasing, constant, or decreasing returns to​ scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor is held​ constant? q=3L+2K

This function exhibits constant returns to scale. For​ example, if L is 2 and K is​ 2, then q is 10. If L is 4 and K is​ 4, then q is 20. When the inputs are​ doubled, output will double. Each marginal product is constant for this production function. When L increases by​ 1, q will increase by 3. When K increases by​ 1, q will increase by 2. -- The production function exhibits constant returns to scale. The marginal product of labor is constant and the marginal product of capital is constant

Convex Isoquant

Within some​ range, a declining number of units of one input can be substituted for a unit of the other​ input, and output can be maintained at the same level. In this​ case, the MRTS is diminishing as we move down along the isoquant.

The production function q=log(L) is associated with

first increasing and then decreasing returns to scale

The production function q=L^2+L is associated with

increasing returns to scale