ECON 323 Test 2

The economic cost of education of a student is the summation of all the economic cost of the resources used by the student in order to obtain his or her education. This includes the time the student dedicates to study. Consider Juana's case. Her tuition is $32,000.00 per year; Juana works part time on a Bookstore and receives $10,000.00 a year for it; if she were going to drop out of college and work full time, Juana would receive $22,000.00 a year. The economic cost of Juana's education (per year) is?

$44,000

John manages his own company and receives $35,000 a year for it. The best salary that John would be able to find in a different company is $90,000 a year. The economic cost of John's labor is:

$90,000

Suppose that a firm has a production function f(L,K)=min{2L,K}. From the following combination of labor and capital (L,K), which one belongs to the same iso-quant as (3,90)?

(5,6)

Consider a firm whose production function is f(L,K)=5L^(1/2)K^(1/2). If K is equal to 1, for what level of labor is the Average Product of Labor equal to 1?

25

Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the average fixed cost of producing q units is?

AF(q)=5/q

Consider the following figure (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a level of K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; five units of labor is shown as reference in the horizontal axis; the corresponding production for this level of labor is 200; the graphs slope is initially increasing, then there is an inflexion point to the left of five levels of labor; after this inflexion point, the slope of the graph is decreasing; a line that passes through zero and is tangent to the graph is also shown; this line is tangent to the graph for a level of labor that is to the left of 5.) From the graph we learn that for the corresponding K:

APL(5,K)=40

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average variable cost of producing q units is?

AVC(q)=1-96/q

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the cost of producing q units is?

C(q)=24+q

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the fixed cost of producing q units is?

F=120.

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average fixed cost of producing q units is?

F=120/q

Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the fixed cost of producing q units is?

F=5

Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). Can we say that the production function satisfies the law of decreasing marginal returns of labor?

False

The following production function represents an industry in which there is free entry: f(L,K)=100L^(1/2)K^(1/3).

False

Consider a firm that has production function f(L,K)=5L^(1/3)K^(2/3). What is the expression for the marginal rate of technical substitution MRTSLK at (L,K)?

K/2L

Consider a firm with production function f(L,K)=3L^(1/3)K^(2/3). Assume that capital is fixed at K=1. Then, the amount of labor necessary to produce q units is?

L(q,1)=q^3/27

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the marginal cost of producing q units is?

MC(q)=1

Consider a firm with production function f(L,K)=3L^(1/3)K^(2/3). Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the marginal cost of producing q units is?

MC(q)=q^2/3

Consider a firm that has production function f(L,K)=5L^(1/3)K^(2/3). What is the expression for this firm's Marginal Product of capital?

MPK(L,K)= 10L^(1/3)/3K^(1/3)

Consider a firm that has production function f(L,K)= 3L^(2/3)K^(1/3). What is the expression for this firm's Marginal Product of capital?

MPK(L,K)= L^(2/3)/K^(2/3)

Consider a firm that has production function f(L,K)=4L^(2/3)K^(1/3). What is the expression for this firm's Marginal Product of labor?

MPL(L,K)= 8K^(1/3)/3L^(1/3)

Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) From the graph we know that for the corresponding K:

MPL(L1,K)>MPL(L2,K)

Consider a newspaper with production function f(L,K)= 4min{L,K}, where L is the units of labor and K the units of capital they use. Is the Average Product of Labor always equal to the Average Product of Capital for this firm?

No

Consider a newspaper with production function f(L,K)= 4min{L,K}, where L is the units of labor and K the units of capital they use. The manager of this firm wants to buy more machines to increase the number of units of output produced by each employee, i.e., the Average Product of Labor. The manager's goal is to increase APL to 10 units of output per unit of labor. Is this possible without finding a new technology to produce?

No

The following figure shows the cost function of a firm. It is a two-axis graph in which the horizontal axis measures production output and the vertical axis measures cost in $. The graph shows and increasing function. The slope of the curve is increasing too. Could this be a cost function for a firm participating in a market in which there is free-entry?

No

The MRTSLK(L,K) for a certain firm is constant and equal to 2. Then, if the firm substitutes 2 units of labor for one unit of capital?

Production increases

A firm's production function associates with each combination of inputs (L,K):

The maximal amount of output that the firm is able to produce with (L,K).

Consider a firm that has production function f(L,K)=5L^(1/3)K^(2/3). Does this production function satisfy the law of decreasing marginal returns of capital?

True

Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure output, in this case articles as in the production function of a newspaper; the graph of the production function, for the given level of capital K fixed, is composed of two line segments; the first goes from the origin to the point (10,30); the second, starting from 10 on, is a horizontal line; it is also shown that the production for five units of labor is 15). Can we say that the production function satisfies the law of decreasing marginal returns of labor?

True

Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure output, in this case units of juice; the graph of the production function is a curve that has decreasing slope in all of its domain.) Can we say that the production function satisfies the law of decreasing marginal returns of labor?

True

The following production function satisfies constant returns to scale: f(L,K)=3L^αK^1-α

True

The following production function satisfies increasing returns to scale: f(L,K)=100LK.

True

Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the variable cost of producing q units is?

VC(q)=q-96

Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the variable cost of producing q units is?

VC(q)=q^3/9.

Consider a firm whose production function is f(L,K)=ALaKb. For which values of A, L,K, a, and b is the Average Product of Labor for this company equal to the Marginal Product of Labor?

a=1 and any values of b, L, and K.

A call center has a production function: f(L,K)=40L+200K. If capital is fixed at K=2, what is the expression for the maximal production as a function of labor?

f(L,2)=40L+400

A call center employs workers and automatic answering machines. Each worker is able to answer a maximum of 5 calls per hour (6 hours a day; a total of 30 calls per day); each automatic answering machine is able to answer a maximum of 10 calls per hour (24 hours a day; a total of 240 calls a day). Denote the number of workers employed by the company by L and the number of automatic answering machines employed by the company by K. The firm's daily production function is?

f(L,K) = 30L + 240K

The following figure shows the production function of a restaurant for a fixed level of capital. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure meals; the graph of the production function is a line that intersects the vertical axis at a positive amount; this graph is a line with positive slope and passes through the point (4,300)). From the following options, which one can be the production function of this restaurant?

f(L,K)=50(L+K)

The following figure shows the marginal and average cost functions of a firm. It is a two-axis graph in which the horizontal axis measures production output and the vertical axis measures marginal and average costs in $. The graph shows a single flat line at level c that is labeled MC=AC. Could this be a marginal cost function for a firm participating in a market in which there is free-entry?

yes

Consider a Cobb-Douglas production function f(L, K)= AL^αK^β, where A, α and β are positive constants. Then, f has increasing returns to scale if:

α+β>1