Topic 4: Production Theory

Which of the following is never negative?

Average product

The production function for the Jason Jax Company is an example of a:

Cobb-Douglas production function

A firm has the following production function: Q = 20L + 20K + 50 What is the scale implication of this production function?

Decreasing returns to scale

The Jason Jax Company has the following long run production function: Q = aL^0.5 K^0.2 E^0.2 The Jason Jax company is facing:

Decreasing returns to scale

If labor and capital have become more and more substitutable over time, then production isoquants have become more like right angles over time. True/False?

False, If labor and capital have become more and more substitutable over time, then production isoquants have become more like straight lines over time.

We should use relatively more labor if we learn that the marginal product per dollar of labor expenditures is less than a marginal product per dollar of capital expenditures. True/False?

False, When MPL /CL < MPK/CK, then we should use relatively more capital compared with labor.

The law of diminishing marginal returns states that increases in the variable input reduce the total product. True/False?

False, increases in the variable input eventually reduce the marginal product of the input.

When marginal product is at its maximum, average product is also at its maximum. True/False?

False. Marginal product hits its maximum before average product hits its maximum. In fact, at the maximum average product output, marginal product equals average product.

The law of diminishing marginal returns is applicable primarily to the long run production function where all inputs are variable. True/False?

False. The law of diminishing returns applies when increasing one factor of production, holding one or more other factors of production constant. In the short run, some factors of production are constant. Hence, we can view the law of diminishing returns as predominantly a short run law.

If the production elasticity for labor is greater than 1, then MP(L) < AP(L). True/False?

False. When the production elasticity for labor is greater than 1, then MPL > APL.

A firm has the following production function: Q = 30L^2 + 25K^2 What is the scale implication of this production function?

Increasing returns to scale

If the average product curve is rising, the marginal product curve:

Must be above the average product curve.

If the labor elasticity of output is 0.65, then the anticipated increase in output for a 3% increase in labor would be approximately 1.95%. True/False?

True, the reason for the word "approximately" is that elasticities are best interpreted for very small changes in the input. Elasticities involve first derivatives that are precise only in the limit.

Growth in number of robots (a form of capital) will increase the marginal product of labor if the production function can be characterized as a power function (Q=aL^bK^c). True/False?

True. Labor becomes more productive, the greater the amount of capital available.

Does the marginal product of energy (E) in the Jason Jax production function depend upon the level capital?

Yes

An isoquant curve shows

all the alternative combinations of two inputs that yield the same maximum total product.

In the presence of a diminishing marginal rate of technical substitution between labor and capital, output can be kept unchanged only if

equal successive increases in labor go hand in hand with ever smaller sacrifices of capital.

A negatively sloped isoquant implies

inputs with positive marginal products.

The combinations of inputs costing a constant C dollars is called:

isocot line

The Rollee Tire Company produces tires for automobiles. In response to increased demand in the market for autos in the United States, the company is considering short-run changes that would allow it to increase production. These might include

overtime work for assembly-line employees.

For any commodity, the relationship between the quantities of various inputs used per period of time and the maximum quantity of the commodity that can be produced is called the

production function.

Suppose that a firm uses two inputs: capital and labor. It has selected the levels of usage of capital and labor at which MPK = 50 and MPL = 20. If the cost of labor is $5 per unit and the cost of capital is $10 per unit:

the firm should increase its usage of capital relative to labor.

The marginal product is defined as:

the incremental change in total output that can be produced by the use of one more unit of the variable input in the production process.

The marginal rate of technical substitution is

the rate at which a producer is able to exchange, without affecting the quantity of output produced, a little bit of one input for a little bit of another input.

A fixed input is an input

whose quantity cannot be changed in the short run.

Production Theory

•Analogous to consumer theory •About physical relation between inputs and outputs •What combinations of inputs lead to specific levels of outputs? •Good for examining implications of adjusting inputs. •Once we understand the "how stuff is made" we can better understand supply curves and how they affect markets.

Production Definitions

•Fixed factors: inputs that a firm cannot cost-effectively change in the short run; e.g., buildings, machinery, land. •Variable factors: inputs that a firm can adjust in the short run; e.g., labor, materials, management. •Short run: period during which at least one factor is fixed •Very short run: period during which all factors are fixed •Long run: period during which the level (and type) of all factors can be adjusted. •Scale: the level of fixed factors employed by a firm.

Returns to Inputs

•Increasing marginal product (increasing returns) from underutilized capital and opportunities for specialization •Decreasing marginal product (decreasing return) when opportunities for better use of capital and specialization are exhausted, crowding might set in. •Law of diminishing returns: when additional units of a variable factor are combined with other fixed factors, marginal product will decline (c.f., diminishing marginal utility).

Factors of production

•Labor, L •Capital, K •Land •Energy •Materials •Management

Analogies for the Relation Between MP and AP

•When MP > AP, then AP is RISING IF YOUR MARGINAL (MOST RECENT) GRADE IN THIS CLASS IS HIGHER THAN YOUR AVERAGE GRADE TO THIS POINT, THEN YOUR CLASS GRADE IS RISING •When MP < AP, then AP is FALLING IF THE MARGINAL WEIGHT ADDED TO A TEAM IS LESS THAN AVERAGE WEIGHT, THEN AVERAGE TEAM WEIGHT DECLINES •When MP = AP, then AP is at its MAX IF THE NEW HIRE IS JUST AS EFFICIENT AS THE AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOES NOT CHANGE