ECON 510 Exam 2 from quizzes

In order to minimize the cost of producing a given level of output, a firm manager should use more inputs when:

that input's price falls

Suppose the production function is given by Q=3K+4L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?

3

The production function is Q = K ^ .4 * L ^ .6 The marginal rate of technical substitution is:

3/2KL^-1

If quantity demanded for sneakers falls by 6 percent when price increases 20 percent, we know that the absolute value of the own price elasticity of sneakers is:

6%/20% 0.3

marginal cost

=

total cost formula

= FC + VC

Which of the following profit functions exhibits a Cobb Douglas production function?

= P (K^0.75 L^0.50) - 20L - 35K

Suppose the demand for good x is ln Qxd = 21 − 0.8 ln Px − 1.6 ln Py + 6.2 ln M + 0.4 ln Ax. Then we know goods x and y are:

complements

Whenever an isoquant exhibits a diminishing marginal rate of technical substitution , the corresponding isoquants are:

convex to the origin

Demand is more inelastic in the short term because consumers:

have no time to find available substitutes

The elasticity that measures the responsiveness of consumer demand to changes in income is the

income elasticity

As we move down along the demand curve, then elasticity of demand becomes more:

inelastic

If there are few close substitutes for a good, demand tends to be relatively:

inelastic

When marginal revenue is negative, demand is:

inelastic

the quantity consumed of a good is relatively unresponsive to changes in price whenever demand

inelastic

What is the value marginal product of labor if: P=$10 , MP L =$25 , and A*P_{L} = 40 ?

$10 x $25 = $250

Suppose that production for good X is characterized by the following production function, Q = k0.5, 0.5, where k is the fixed input in the short run. If the per-unit rental rate of capital, r, is $25 and the per-unit wage, w, is $15, then the fixed cost of using 81 units of capital and 9 units of labor is:

$2,025

The demand for good X has been estimated by

-0.6

The production function for a competitive firm is Q = K ^ .5 * L ^ .5 . The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing quantity of labor is:

1

The demand for good X has been estimated to be ln Qxd = 100 - 2.5 ln PX + 4 ln PY + ln M. The income elasticity of good X is:

1.0

Suppose you are a manager of a factory. You purchase five (5) new machines at one million dollars each. If you can resell two of the machines for $500,000 each and three of the machines for $200,000 each, what are the sunk costs of purchasing the machines ?

2($500,000) - 3($200,000) = $3.4 million

What would the average and marginal cost curve look like under constant returns to scale?

Average and marginal cost curve are the same curve and are flat (constant).

Suppose the production function is given by Q=3K+4L. What is the average product of capital when 10 units of capital and 10 units of labor are employed?

Average product of capital = Total product/Capital Output = 3K+4L = 3(10)+4(10) = 70 Capital = 10 units Average product = 70/10 =7

For the cost function C(Q) = 500 + 12Q + 4Q^2 + Q^3, what is the marginal cost of producing the eighth unit output?

C(Q)= 500 + 12Q + 4Q^2 + Q^3 MC= dC/dQ = 12+8Q+3Q^2 MC(8) = 268

Economies of scope exist when:

C(Q1) + C(Q2) > C(Q1,Q2)

the production function Q = L^5K^5 is called:

Cobb Douglas

When marginal cost curve is below an average cost curve, average cost is:

Declining with output

Suppose the own price elasticity of demand for good X increases by 5 percent. What would you expect to happen to the total expenditures on good X?

Decrease

What is implied when the total cost of producing Q_{1} and Q_{2} together is less than the total cost of producing Q_{1} and Q_{2} separately ?

Economies of scope

A firm derives revenue from two sources: goods X and Y. Annual revenues from good X and Y are $10,000 and $20,000, respectively. If the price elasticity of demand for good X is -2.0 and the cross-price elasticity of demand between Y and X is 1.5 then a 4 percent price decrease will:

Ex = -2 = % change in Qx / % change in Px % change in R = % change in Qx + % change in Px = -8% + 4% =-4% =-4 * 10,000 = -400 = (1.5)(4%)(20,000) = 1200 = 1200 - -400 = 800 increase total revenues from X and Y by $800

Suppose the cost function is C(Q)=50+Q-10Q^ 2 +; 2Q ^ 3 . At 10 units of output , the average cost curve is :

I'm the increasing stage

For the cost function C(Q) = 100 + 2Q + 3Q^2, the average fixed cost of producing 2 units of output is:

In the TC function, TFC = 100. AFC = TFC/Q = 100 / 2 = 50

Suppose the w=$20 and r=$30. The isocost line for a firm in this industry is:

K = 0.033C − 0.66L

For the cost function C(Q) = 100 + 2Q + 3Q^2, the marginal cost of producing 2 units of output is

MC is the first order derivative of TC function. MC = 2 + 6Q When Q = 2 MC = 2 + 6(2) = 14

Which of the following sets of economic data is minimizing the cost of producing a given level of output?

MPL = 20, MPK = 40, w = $16, r = $32.

The production function is Q = K ^ .6 * L ^ .4 The marginal rate of technical substitution is:

MRTS = MPL/ MPK MPL = dQ/dL = .4 x K^.6 x L^-.6 MPK = dQ/dK = .6 x K^-.4 x L^.4 MRTS = .4K/.6L MRTS = 2K/3L

Firm managers should use inputs at levels where the:

Marginal benefit equals marginal cost and value marginal product of labor equals wage

The isoquants are normally drawn with a convex shape because inputs are :

Not perfectly substitutable

When there are economies of scope between products, selling off an unprofitable subsidiary could lead to:

Only a minor reduction in costs

Suppose Qxd = 10,000 - 2 Px + 3 Py - 4.5M, where Px = $100, Py = $50, and M = $2,000. What is the own price elasticity of demand?

Qxd = 10000 - (2 x 100) + (3 x 50) - (4.5 x 2000) = 950 d(Qxd)/dPx = -2 Own price elasticity = [d(Qxd)/dPx]*Px/Qxd = -2*100/950= -0.21

Suppose Qxd = 10,000 - 2 Px + 3 Py - 4.5M, where Px = $100, Py = $50, and M = $2,000. How much of good X is consumed?

Qxd= 10,000- 2(100) +3(50)- 4.5(2000) = 10,000-200+150-9000 = 950

The marginal product of an input is defined as the change in:

Total output attributable to the last unit of an input

It is profitable to hire labor so long as the:

VMPL is greater than wage

The demand for labor by a profit-maximizing firm is determined by:

VMPl = W

The costs of production include:

accounting costs and opportunity costs

An income elasticity less than zero tells us that the good is:

an inferior good

Which curve(s) does the marginal cost curve intersect at the (their) minimum point?

average total cost curve and average variable cost curve

Average fixed cost:

declines continually as output is expanded

When marginal cost curve is below an average cost curve, average cost is:

declining with output

Assume that the price elasticity of demand is -0.75 for a certain firm's product. If the firm lowers price, the firm's managers can expect total revenue to:

decrease

When marginal revenue is positive for a linear (inverse) demand function, decreases in output will cause total revenues to:

decrease

A study has estimated the effect of changes in interest rates and consumer confidence on the demand for money to be: log M = 14.666 + .021 log C - .036 log r, where M denotes real money balance. C is an index of consumer confidence, and r is the interest rate paid on bank deposits. Based on this study, a 5% increase in interest rates will cause the demand for money to:

decrease by 0.036*0.05=0.0018

Assume that the price elasticity of demand is -2 for a certain firm's product. If the firm raises price, the firm's managers can expect total revenue to:

decreases

When the own price elasticity of good X is -3.5, then total revenue can be increased by:

decreasing the price

Suppose the long-run average cost curve is U-shaped. When LRAC is in the increasing stage, there exist:

diseconomies of scale

Larger firms can produce a product at lower average cost than small firms when:

economies of scale exist

If apples have an own-price elasticity of -1.2 we know the demand is:

elastic

When marginal revenue is positive, demand is:

elastic

the combinations of inputs that produce a given level output are depicted by:

isoquants

If the Marginal product per dollar spent on capital is less than the marginal product per dollar spent on labor, then in order to minimize costs the firm should use:

less capital and more labor

We would expect the own price elasticity of demand for food to be:

less elastic than the demand for cereal.

The change in total output attributable to the last unit of an input is the:

marginal product

Total product begins to fall when:

marginal product is zero

We would expect the demand for jeans to be:

more elastic than the demand for clothing.

Which of the following statements is incorrect?

none of the statements is correct

If the last unit of input increases total product, we know that the marginal product is:

positive

Which of the following factors would NOT affect the own price elasticity of a good?

price of an input

Lemonade, a good with many close substitutes, should have an own price elasticity that is:

relatively elastic

A production function:

represents the technology available for turning inputs into outputs

Fixed costs exist only in:

short run

You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w=$40, r=$100, MP L =20, and M*P_{K} = 40 the firm:

should use more L and less K to cost minimize.

Changes in the price of an input cause:

slope changes in the isocost line.

Costs that are forever lost after that have been paid are:

sunk costs

Which of the following is NOT an important factor that affects the magnitude of the own price elasticity of a good?

supply of the good

When the price of sugar was "low," U.S. consumers spent a total of $3 billion annually on sugar consumption. When the price doubled, consumer expenditures increased to $5 billion annually. This data indicates that:

the demand for sugar is inelastic

The long run is defined as:

the horizon in which the manager can adjust all factors of production

an isoquant defines the combination of inputs that yield the producer

the same level of output

When marginal revenue is zero, demand will be:

unit elastic

If the demand for a product is Qxd = 10 - lnPx, then product x is:

unitary elastic

Which of the following profit functions exhibits a Leontief production function ?

π = P x min x (2L, 5K) - 20L - 35K

Suppose the demand for good x is ln Qxd = 21 − 0.8 ln Px − 1.6 ln Py + 6.2 ln M + 0.4 ln Ax. Then we know that the own price elasticity for good x is:

inelastic

The demand for food (a broad group) is more:

inelastic than the demand for beef (specific commodity).

Costs that change as output changes are:

variable costs

Suppose the marginal product of labor is 8 and the marginal product of capital is 2. If the wage rate is $4 and the price of capital is $2, then in order to minimize costs the firm should use :

More labor and less capital

The management of Local Cinema has estimated the monthly demand for tickets to be ln Q = 22,328 - 0.41 ln P + 0.5 ln M - 0.33 ln A + 100 ln PDVD, where Q = quantity of tickets demanded, P = price per ticket, M = income, A = advertising outlay, and PDVD = price of a DVD rental. It is known that P = $5.50, M = $9,000, A = $900, and Pvcr = $3.00. Based on the information given, which of the following statements is false?

Movies are complements for DVD rentals.

The production function for a competitive firm is Q =; K ^ .5 * L ^ .5 The firm sells its output at a price of $10, and can hire labor at a wage of $5. Capital is fixed at one unit. The profit-maximizing quantity of labor is:

1

Suppose you are a factory manager. You purchase 5 new machines at 1 million dollars each. You can resale 2 of the machines at $500,000 and the other three at $200,000. What are the sunk costs of the purchase of machines?

1,000,000-(2 x 500,000)-(3 x 200,000)=3.4 million

Suppose the production function is Q=min{K,2L}. How much output is produced when 4 units of labor and 9 units of capital are employed ?

2(4)=8

The demand for good X has been estimated to be ln Qxd = 100 - 2.5 ln PX + 4 ln PY + ln M. The cross-price elasticity of demand between goods X and Y is:

4.0

The demand for good X is estimated to be Qxd = 10,000 - 4PX + 5PY + 2M + AX where PX is the price of X, PY is the price of good Y, M is income, and AX is the amount of advertising on X. Suppose the present price of good X is $50, PY = $100, M = $25,000, and AX = 1,000 units. What is the demand curve for good X?

61,500 - 4Px

The demand for which of the following commodities is likely to be most inelastic?

Beverages

Which of the following profit functions exhibits a linear production function ?

Profit = P x (3K + 4L) - 20L -35K

Give an example of a production function that exhibits constant returns to scale

Q = K + L OR Q = K^(1/2)L^(1/2), OR 1 = min {K,L}

For the cost function C(Q) = 100 + 2Q + 3Q^2, the variable cost of producing 2 units of output is

TVC = 2Q + 3Q2 At Q = 2 TVC = 2(2) + 3(2)2 = 16

Which of the following conditions is true when a producer minimizes the cost of producing a given level of output?

The MRTS is equal to the ratio of input prices, and the marginal product per dollar spent on all inputs is equal

If a firm's production function is Leontief and the wage rate goes up, the:

cost minimizing combination of capital and labor does not change.

the elasticity that measures the responsiveness of demand for a good due to changes in the price of a related good is the:

cross-price elasticity

As the usage of an input increases, marginal product:

initially increases then begins to decline

Isoquants are normally drawn with a convex shape because:

inputs are not perfectly substitutable

Since most consumers spend very little on salt, a small increase in the price of salt will:

not reduce quantity demanded by very much

A price elasticity of zero corresponds to a demand curve is:

vertical

Which curve(s) does the marginal cost curve intersect at the (their) minimum point?

Average total cost curve and average variable cost curve

Suppose the cost function is C(Q) = 50 + Q - 10Q^2 + 2Q^3. What is the total cost of producing 10 units?

The correct answer is (d) $1,060 Total Cost of producing Q units is given by: C(Q) = 50 + Q − 10Q2 + 2Q3 Hence Total Cost of Producing 10 units = C(10) => C(10) = 50 + 10 − 10*102 + 2*103 = 1060

Suppose the cost function is C(Q) = 50 + Q - 10Q^2 + 2Q^3. What is the variable cost of producing 10 units?

Variable cost= Q - 10Q^2 + 2Q^3 When Q= 10 Variable cost= 10 - 10(10)^2 + 2(10)^3 = 1010

If the production function is Q = K^5L^5 and capital is fixed at 1 unit, then the average product of labor when L = 36 is:

1/6