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ECON 2010 Lecture Notes - Lecture 11: Kolmogorov Space, Isoquant, Isocost

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School
Memorial University
Department
Economics
Course
ECON 2010
Professor
nikitalyssenko

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Document Summary

Lecture 7. 3 marginal rate of technical substitution. Suppose that at the moment we are using (x1, x2) to produce q units. In fact, to answer this question, we want to compute the marginal product of factor: mp1= q/ x1. The marginal product is the rate: additional output per units of extra input. We can also write down the expression for the marginal product of factor 2: mp2= q/ x2. Assume we want to drop a little bit of factor 1. To produce as much output as before, we should add a bit more factor 2 to (cid:862)co(cid:373)pe(cid:374)sate(cid:863) for the decrease in factor 1. Note: the concept of mrts is like marginal rate of substitution examined in consumer theory. It is(cid:374)"t hard to demonstrate that the slope of isoquant equals to the ratio of marginal products and hence mrts: mrts= mp1/mp2=slope of isoquant.

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Related Questions

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

 

Question 1

 

A firm should hire workers up to the point where
 

Question 1 options:

 
MP = P.
 
MFC = P.
 
MFC = MRP.
 
MP = MRP.
 

Question 2

 

If the additional revenue from hiring an additional worker equals the additional costs from hiring the extra worker, then we know that
 
Question 2 options:
 
MFC/MPPL = wage.
 
MFC/MRPL = 1.
 
MFC = MPPL.
 
MRPL/P = MFC.
 

Question 3

A firm that maximizes profits also
 
Question 3 options:
 
pays input prices lower than other firms do.
 
cuts corners in production processes so that its products are made too cheaply.
 
is inefficient.
 
uses the least-cost combination of resources.

Question 4

The demand curve for labor slopes down because
 
Question 4 options:
 
firms value less efficient workers less than they value more efficient workers.
 
firms must lower prices to sell the additional units of its product that the extra workers produce.
 
of profit maximizing behavior.
 
of the law of diminishing marginal product.

Question 5

If MFC > MRPL, the firm should
 
Question 5 options:
 
get rid of some capital.
 
reduce the number of workers.
 
lower wages.
 
hire more workers.

Question 6

Which of the following will not lead to an increase in the demand for labor for a firm producing automobiles?
 
Question 6 options:
 
A decrease in labor productivity.
 
A decrease in the price of automobiles.
 
A decrease in the price of robots that are used to solder parts of the car together.
 
An increase in the demand for automobiles.

Question 7

 
The marginal revenue product gives
 
Question 7 options:
 
the additions to total cost when an additional unit of a variable input is hired.
 
the additional revenue obtained when an additional unit of a variable input is hired.
 
the change in total product for an additional unit of a variable input.
 
the amount that other inputs must increase by when labor increase by one unit.

Question 8

The monopolist's input demand curve is the
 
Question 8 options:
 
marginal physical product curve.
 
marginal revenue product curve.
 
marginal revenue curve.
 
marginal factor cost.

Question 9

An increase in product price implies that
 
Question 9 options:
 
the firm's demand for labor increases.
 
the firm's demand for labor decreases.
 
the wage rate the firm pays will increase.
 
the firm's marginal factor cost will increase.

Question 10

Which of the following will not lead to a change in the demand for labor?
 
Question 10 options:
 
A change in the supply of labor.
 
A change in demand for the final good.
 
A change in the price of a substitute input.
 
A change in labor productivity.

3. A firm has a long-run production function:   

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run? 

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?