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peachzebra922Lv1

28 Sep 2019

The Marginal Productivity of Labor (MPL) is defined as dY/dL, meaning it measures how much more output (Y) is produced with one more additional unit of Labor (L). Likewise, the Marginal Productivity of Capital (MPK) is defined as dY/dK, meaning it measures how much more output (Y) is produced with one more additional unit of Capital (K). MPL and MPK respectively are equal to wage and to rent given our assumption that compensation equals productivity.
Given the following information please find the wage and rent rate: Y=1/2L^1/4K^3/4 and L=64 and K=256

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Insha FatimaLv10

28 Sep 2019

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Related questions

For each of the following assertions, please indicate whether they are true or false. No credit will be given without an explanation as to why your claim is correct.

(a) (4 points) There are two firms: one has production function f (K, L) = K + L and the other has production function f?(K,L) = (K+L)2 ?50. Assertion: These two firms have the same shaped isoquants, but different technology.

(b) (4 points) Assertion: In the short run, if the marginal product of labor curve is decreasing, then it is below the average product of labor curve.

(c) (4 points) A T-shirt company can make 1000 T-shirts with 2 workers and 1 machine. It continues to make 1000 T-shirts if it has more than 2 workers but only 1 machine or 2 workers and more than 1 machine. The company currently produces 1000 shirts per month for its single customer. The price of capital falls, but the firm must still produce 1000 shirts per month. Let all inputs be variable. Assertion: The firm will not hire or fire any workers.

(d) (4 points) A technology firm has a Cobb Douglas production function and measures the marginal rate of technical substitution (MRTSLK) at MPL/MPK = 3. The prices of labor and capital faced by the firm are such that currently W/R = 2. Assertion: The tech firm can lower costs (holding output fixed) by laying off some of its labor force and using more capital.

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

Suppose the process of producing lightweight parkas by Polly's Parkas is described by the function:

q = 40K^0.6 (L-40)^0.4

where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $10 worth of raw materials are used in the production of each parka.

Note that Eq/EK = 40(0.6) K ^-0.40 (L-40)^0.4 and Eq/EL = 40K ^0.6 (0.4) (L-40) ^-0.60

By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates of machines (r).

The cost-minimizing demands for K and L are:

Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost. The total cost function (TC) is:

2. This process requires skilled workers, who earn $64 per hour. The rental rate on the machines used in the process is $16 per hour. At these factor prices, what are total costs as a function of q.

Total costs (TC) are:

Does the technology exhibit decreasing, constant, or increasing returns to scale?

3. Polly's Parkas plans to produce 2000 parkas per week. At the factor prices given above, how many workers should the firm hire (at 40 hours per week) and how many machines should it rent?

The firm should use ___ worker hours.

The firm should use ___ machine hours.

What are the marginal and average costs at this level of production?

Marginal cost is $___ per unit of output.

Average cost is $___ .