Economics 2150A/B Lecture 6: Chapter 6

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22 Jun 2018

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Chapter 6: Inputs and Production Functions

Total Product Function: A Single-Input production function. It shows how total output depends on the

level of the input

oIncreasing Marginal Returns to Labor:

An increase in the quantity of labor

increases total output at an increasing

rate.

oDiminishing Marginal Returns to

Labor: An increase in the quantity of

labor increases total output but at a

decreasing rate.

oDiminishing Total Returns to Labor: An

increase in the quantity of labor

decreases total output.

Marginal Product: Is the change in the output that results from a small change in an input holding the

levels of all other inputs constant.

oCan be used to calculate the effect of each varying input individually by holding the other

constant (K or L)

oMPL = Q/L (holding constant all other inputs)

oMPK = Q/K (holding constant all other inputs)

Example: Q = K1/2L1/2

MPL = (1/2)L-1/2K1/2

MPK = (1/2)K-1/2L1/2

Average Product: is equal to the total output that is to be

produced divided by the quantity of the input that is used in its

production:

oAPL = [K1/2L1/2]/L = K1/2L-1/2

oAPK = [K1/2L1/2]/K = L1/2K-1/2

Isoquant: traces out all the combinations of inputs (labor and capital) that allow that firm to produce the

same quantity of output

oEvery input combination of labor and capita along the same indifference curve produces the

same output

oEach isoquant corresponds to progressively higher outputs

Marginal rate of technical substitution: measures the amount of input, L, the firm would require in

exchange for using a little less of another input, K, in order to just be able to produce the same output as

before

oMRTSL,K = - K/L (for a constant level of output)

oMarginal products and the MRTS are related:

MPL(L) + MPK(K) = 0

MPL/MPK = -K/L = MRTSL,K

M ULM UKQ )()(

+=

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Document Summary

It shows how total output depends on the level of the input: increasing marginal returns to labor: An increase in the quantity of labor increases total output at an increasing rate: diminishing marginal returns to. Labor: an increase in the quantity of labor increases total output but at a decreasing rate: diminishing total returns to labor: an increase in the quantity of labor decreases total output. Average product: is equal to the total output that is to be produced divided by the quantity of the input that is used in its production: apl = [k1/2l1/2]/l = k1/2l-1/2, apk = [k1/2l1/2]/k = l1/2k-1/2. K: unique value at each point along the graph. Perfect substitutes: have straight ppf"s as they can be substituted freely without losing utility. Perfect complements: the inputs must be combined at the given fixed proportion to be used: a production function where the inputs must be combined in fixed proportion is called a fixed- proportions production function.

Related Questions

Use the following information on a hypothetical short-run production function to answer questions A-C.

The price of labor is $20 per day.

Ten units of capital are used each day, regardless of output level.

The price of capital is $50 per unit.

(A). Calculate the marginal product (MP) and average variable product (AP) of each unit of labor input.
(B). Calculate total (TC), average total (ATC), average variable (AVC), and marginal costs (MC).
(C). Can you tell where diminishing marginal returns sets in?

Labor (L)	Output (Q)	MP	AP	TC	ATC	AVC	MC
5	120	--					--
6	140
7	155
8	165
9	168

harlequinotter496

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