ECON 2009 Chapter Notes - Chapter 5: Marginal Product, Second Derivative, Production Function

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If x1 is the level of the first input and x2 is the level of the second input, the production function is. Variable inputs can be changed in the short run (e. g. labor) In the long run all inputs are variable. The production function shows the relationship between output and input. To know how output changes as the number of input varies, we can use. Average product- estimating the units of output, on average per unit. Marginal product (mp) incremental change in output created by a small change in input. The marginal product of an input is the derivative of output with regard to the quantity of the input. Second derivative (dq/dl) assumes that a manager can employ labor continuously, as in 1. 25 workers or 1. 33 workers. Can be achieved through part time or workers who work more or less time than in advance day"s work.

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The law of eventually diminishing marginal returns: (Points : 1)

a. states that each and every increase in the amount of the variable factor employed in the production process will yield diminishing marginal returns.
b. is a mathematical theorem that can be logically proved or disproved
c. is the rate at which one input may be substituted for another input in the production process
d. None of the above

The marginal product is defined as: (Points : 1)

a. the ratio of total output to the amount of the variable input used in producing the output
b. 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
c. the percentage change in output resulting from a given percentage change in the amount of the variable input X employed in the production process with Y
d. None of the above

The rate at which one input X may be substituted for another input Y in a production process, while total output remains constant, is: (Points : 1)

a. the slope of the isoquant curve
b. the marginal rate of technical substitution

c. equal to MPx/MPy

d. all of the above
e. none of the above

Marginal revenue product is: (Points : 1)

a. defined as the amount that an additional unit of the variable input adds to the total revenue
b. equal to the marginal factor cost of the variable factor times the marginal revenue resulting from the increase in output obtained
c. equal to the marginal product of the variable factor times the marginal product resulting from the increase in output obtained
d. a and b
e. a and c

Marginal factor cost is defined as the amount that an additional unit of the variable unit of the variable input adds to ____________. (Points : 1)

a. marginal cost
b. variable cost
c. marginal rate of technical substitution
d. total cost
e. none of the above

In the Cobb-Douglas production function Q=aL^?1.K^?2 ______________. (Points : 1)

a. the marginal product of labor (L) is equal to ?1
b. the average product of labor (L) is equal to ?2
c. if the amount of labor input (L) is increased by 1 percent, then output will increase by ?1 percent
d. a and b
e. a and c

The short-run cost function is: (Points : 1)

a. where all inputs to the production process are available
b. relevant to decisions in which one or more inputs to the production process are fixed
c. not relevant to optimal pricing and production output decision facilities
d. crucial in making optimal investment decisions in new production facilities
e. none of the above

Theoretically, in a long-run cost function: (Points : 1)

a. all inputs are fixed
b. all inputs are considered variable
c. some inputs are always fixed
d. capital and labor are always combined in fixed proportions

A linear total cost function implies that: (Points : 1)

a. marginal costs are constant as output increases
b. average total costs are continually decreasing as output increases
c. a and b
d. none of the above

Consider a profit-maximizing firm with the following production function: f(ï¨x1,x2) = ½x1x2.

The prices of the two inputs are equal to w1= 4 and w2= ½ 2, respectively

.a) What are the returns-to-scale properties of the firmâs production technology. Prove your answer.

.b) What input combination should the firm use to produce Q units of output?

.c) What is the firm's total cost of production as a function of the amount of output, Q?

.d) What is its marginal and average cost of production?

.e) Suppose the price of the first input falls to $2. What input combination should the firm use

now to produce Q units of output? What is its total, marginal, and average cost of production?

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1. The slope of the total product curve measures

a. the marginal rate of technical substitution.

b. marginal product.

c. average product.

d. the maximum average product.

e. minimum product.

2. The Law of Diminishing Returns to a variable input (such as labor) assumes that

a. there is at least one fixed input.

b. all inputs are changed by the same percentage.

c. the firm is operating in the short run.

d. all inputs are held constant.

e. a and c.

3. An isoquant curve identifies

a. the maximum output possible, given a fixed budget.

b. the different combinations of goods the can be produced, given fixed amounts of inputs.

c. the different combinations of inputs that can be used to produce a fixed rate of output.

d. none of the above.

4. The ratio of total productivity to the total quantity of a variable input being used in production is

a. equal to marginal physical productivity of the input.

b. constant as employment levels of the input vary.

c. equal to average physical productivity of the input.

d. equal to the marginal rate of technical substitution.

ECON 2009 Chapter Notes - Chapter 5: Marginal Product, Second Derivative, Production Function

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