econ 321 exam #2

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Suppose the market supply curve is Q = p/5. At a price of 10, producer surplus equals

$10 -solve for q = 10/2 = 5 -s curve starts at 0, so PS = 1/2(10)(2)

Suppose the market supply curve is Q = p - 5. At a price of 10, producer surplus equals

$12.5 -q= 10-5 =5 -graph s curve -s curve starts at $5 so PS = 1/2(10-5)(5)

Suppose C = 10 + 0.1Q^2 for a competitive firm. If p* = 10, the firm's profits will be

$240 -set MC=P -solve for Q (50) -plug Q into profit equation = R - C

When a firm produces one unit, the variable cost is $3. When the firm produces two units, the variable cost is $6. What is the marginal cost associated with two units of production?

$3 -MC=change in Q/change in L -(6-3)/(2-1)

Mr. Jones was selling his house. The asking price was $220,000, and Jones decided he would take no less than $200,000. After some negotiation, Mr. Smith purchased the house for $205,000. Jones' producer surplus is

$5,000 -PS = (205,000-200,000)

Joe's demand for spring water can be represented as Q = 10 - p (where p is measured in $/gallon and Q is measured in gallons). He recently discovered a spring where water can be obtained free of charge. His consumer surplus from this water is

$50 -his CS is the entire triangle since p=0

To produce a recorded​ Blu-ray disc, q=​1, a firm uses one blank​ disc, D=​1, and the services of a recording​ machine, M=​1, for one hour. Draw an isoquant for this production process. Explain the reason for its shape. Graph is L shaped (1,1) (2,1) (3,1) (4,1) and (1,1) (1,2) (1,3) (1,4) The isoquant has this shape because

A. the firm cannot substitute between discs and machines.

Which of the following statements is NOT true?

AVC = wage/MPL

Use the tangency rule to determine the​ cost-minimizing bundles of labor and capital for a Japanese synthetic rubber​ firm's production​ function, q=L^0.5K^0.5​, where w=​$40 and r=​$40. At the​ cost-minimizing bundle as a function of​ L, How does your answer change if w=​$80 and r=​$20​? At the​ cost-minimizing bundle as a function of​ L,

K = L K = 2L

Use the tangency rule to determine the​ cost-minimizing bundles of labor and capital for a Japanese synthetic rubber​ firm's production​ function, q=L0.5K0.5​, ​(Flath, 2011), where w=​$160 and r=​$40. At the​ cost-minimizing bundle as a function of​ L, How does your answer change if w=​$640 and r=​$20​? At the​ cost-minimizing bundle as a function of​ L,

K=4L -use Q equation to find MPl/MPk and set equal to W/R K=32L

Returns to scale refers to the change in output when

all inputs increase proportionally

Economists define a market to be competitive when the firms

are price takers

Mary purchased a stuffed animal toy for $5. After a few weeks, someone offered her $100 for the toy. Mary refused. One can conclude that Mary's consumer surplus from the toy is

at least $95.

The short run is a period when

at least one input is fixed

What is the effect of a​ lump-sum franchise tax of t on the quantity at which a​ firm's after-tax average costLOADING... curve reaches a​ minimum? ​ (Assume that the​ firm's before-tax average cost​ curve, ACBT​, is​ U-shaped.) Determine the average tax per unit of output. For​ example, if the firm sells only 1 unit of​ output, then its average cost in taxes is equal to If the firm sells 500 units of​ output, then its average cost in taxes is equal to Determine the effect of the tax on the marginal cost curve. Compare the quantities at which the two average cost curves reach minimums.

average tax =t/q 1 unit = t t/500 after tax curve is high than before tax curve The tax will not affect the marginal cost curve. The quantity at which the average cost curve with the franchise tax ​(ACAT​) reaches a minimum is greater than the quantity at which the average cost curve without the franchise tax ​(ACBT​) reaches a minimum.

In deciding whether to operate in the short run, the firm must be concerned with the relationship between price of the output and

average variable cost.

In the​ short-run, a firm cannot vary its​ capital, K=​4, but can vary its​ labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the​ short-run if its production function is q=10L+K. Note that ​dq/dL=10. In the​ short-run, the firm

will not experience diminishing marginal returns to labor because​ labor's marginal product is constant. will not experience diminishing marginal returns to labor because​ labor's marginal product equals 10.

An isoquant represents levels of capital and labor that

yield the same level of output

A Japanese synthetic rubber​ firm's production function is given​ by: q=L^0.3K^0.7​, Use the tangency rule to determine the​ cost-minimizing bundle of labor and capital to produce q​ = 10 given that the input prices​ are: w=​$6 and r=​$7. At the​ cost-minimizing bundle​

​L=6.2, K=12.4 -plug values into cost equation -solve for MPl/MPk and set equal to w/r -solve for k and plug into quantity equation

By how much does the residual elasticity of demand facing a firm increase as the number of firms increases by one​ firm? The effect of a change in the number of firms on the residual elasticity of demand for a firm as a function of the number of firms​ (n), the market elasticity of demand ​(ε​), and the supply elasticity of the other firms ​(ηo​) is

∂εi/∂n=ε−ηo.

Suppose a firm is currently operating in a​ short-run time frame and the production function of the firm is given by Q=L^0.5K^0.5. Assume that the wage rate is​ $2 and the rental rate is​ $5 and the amount of fixed capital in the​ short-run is 2. Find the total cost​ function/equation for the firm.

c=10+q^2 c=wL +rK -plug w and k and r into equation -use quantity equation to solve for L -plug l into cost equation

Suppose that q=30​, L=4​, and K=25 is a point on the production function q=​f(L, K). Is it possible for q=30​, L=4​, and K=26 to also be a point on this production​ function? Why or why​ not? The combination q=30​, L=4​, and K=26

cannot be a point because we assume production functions are efficient.

Efficient production occurs if a firm

cannot produce its current level of output with fewer inputs

The slope of the isocost line tells the firm how much

capital must be reduced to keep total cost constant when hiring one more unit of labor.

The slope of the isoquant tells the firm how much

capital must decrease to keep output constant when labor increases by one unit

What types of firms allow owners of a firm to obtain the advantages of limited​ liability? Owners have limited liability in

corporations.

If a profit-maximizing firm finds that, at its current level of production, MR < MC, it will

decrease output.

​Michelle's business produces ceramic cups using​ labor, clay, and a kiln. She produces cups using a fixed proportion of labor and​ clay, but regardless of how many cups she​ produces, she uses only one kiln. She can manufacture 20 cups a day with one worker and 28 with two workers. Does her production process illustrate decreasing returns to scale or a diminishing marginal​ returns? ​Michelle's production process illustrates What is the likely explanation for why output might not increase proportionately with the number of​ workers?

diminishing marginal returns The amounts of other inputs are held constant.

Why would high transaction costs or imperfect information tend to prevent​ price-taking behavior? High transaction costs and imperfect information would prevent​ price-taking behavior because they

discourage customers from buying from rival firms.

In the long run, fixed costs

don't exist

Assume a consumer has a horizontal demand curve for a product. His consumer surplus from buying the product

equals zero

In a perfectly competitive​ market,

firms can freely enter and exit

In a perfectly competitive market,

firms can freely enter and exit.

A special license is required to operate a taxi in many cities. The number of licenses is restricted. More drivers want licenses than are issued. This describes a non-perfectly competitive market because

firms cannot freely enter and exit the market.

Suppose that the price of K goes up. Intuitively, what should happen to the least-cost L and K combination for producing € Q?

firms uses less of K and L increases more than before

The difference between a fixed and a variable input is that a

fixed input cannot practically vary in the short run and a variable input can easily vary during the relevant period.

Suppose that once a well is dug, water flows out of it continuously without any additional effort. Customers collect their water and pay a per gallon fee when they leave the site of the well. In the short run, the competitive firm in this market

has no variable costs.

A firm might not seek to maximize profit if instead its primary goal is to

have fancy offices.

Suppose a firm can only vary the quantity of labor hired in the short run. An increase in the cost of capital will

have no effect on the firm's marginal cost.

Firms that exhibit price-taking behavior

have outputs that are too small to influence market price and thus take it as given

If a profit-maximizing firm finds that, at its current level of production, MR > MC, it will

increase output

The production function is a relationship between

inputs and outputs

The above figure shows the short-run production function for Albert's pretzels. The marginal productivity of labor

is less than or equal to the average productivity of labor for all amounts of labor

A firm should always shut down if its revenue is

less than its avoidable costs.

Economists typically assume that the owners of firms wish to

maximize profits

If a firm operates in a perfectly competitive market, then

no firms will advertise.

Suppose C = 10 + 0.1Q2. If p*=10 and there are 100 identical firms in a competitive market, the market supply will be

none of the above

Mister Jones was selling his house. The asking price was $220,000, and Jones decided he would take no less than $200,000. After some negotiation, Mister Smith purchased the house for $205,000. Smith's consumer surplus is

not able to be calculated from the information given.

In the long run, all factors of production are

variable

Suppose the firm faces a price of ​$38​, an average variable cost of ​$28​, and has an average fixed cost of ​$5. In the​ short-run, the firm

will earn an economic profit

Explain why the firm will or will not experience diminishing marginal returns to labor in the​ short-run if its production function is q=L^1/2K^1/2. Note that ​dq/dL=0.5L^−1/2K^-1/2. In the​ short-run, the firm

will experience diminishing marginal returns to labor because​ labor's marginal product equals 0.5L^−1/2K^-1/2.

​Meredith's firm sends her to a conference for managers and has paid her registration fee. Included in the registration fee is free admission to a class on how to price derivative securities such as options. She is considering​ attending, but her most attractive alternative opportunity is to attend a talk by Warren Buffett about his investment​ strategies, which is scheduled at the same time. Although she would be willing to pay ​$110 to hear his​ talk, the cost of a ticket is only ​$60. Given that there are no other costs involved in attending either​ event, what is​ Meredith's opportunity costLOADING... of attending the derivatives​ talk? To calculate her opportunity​ cost, determine the benefit that Meredith would forego by attending the derivatives class. The opportunity cost of the derivatives talk for Meredith is ​$ Suppose instead that Meredith has already paid the ​$60 price for the ticket to the Warren Buffett talk and that the ticket cannot be​ re-sold. That​ is, assume the ticket is a sunk cost ] Now what is the opportunity cost of the derivatives talk for​ Meredith? The opportunity cost of the derivatives talk for Meredith is ​$

$50 (110-60) $110 (60+50)

Consider the following production​ function: q = 7LK + 5L^2 − (1/3)L^3. Assuming capital is plotted on the vertical axis and labor is plotted on the horizointal​ axis, determine the value of the marginal rate of technical substitution when K​ = 20 and L​ = 10. ​ MRTS​ =

-2

A change in relative input prices will always result in

-a change in the slope of the isocost lines. -a tangency between a new isocost line and the isoquant. -a rotation of the isocost lines. (Rotation means a shift that's not parallel.) D) All of the above.

If a firm (either competitive, monopoly or oligopoly) is producing some output level Q* according to the profit-maximizing rule and the shutdown condition is not satisfied, then which of the following is true:

-if the firm is making some profit, it is the highest possible profit. -if the firm is making some loss, it is the lowest possible loss. -the firm should keep producing Q*. All of the above.

Using the information from Deadweight Loss from Wireless Taxes, draw graphs to illustrate why the tax on landlines creates no deadweight loss while the tax on cell phones creates a more substantial deadweight loss. Part 2 ​1.) Use the line drawing tool to draw the demand for landline minutes. Label this line​ 'landline'. ​2.) Use the line drawing tool to draw the demand for wireless minutes. Draw the curve such that wireless​ demand, landline demand and supply intersect at the same point. Label this line​ 'wireless'. ​3.) Use the point drawing tool to indicate the initial equilibrium. Label this point ​'E1​'. ​4.) Use the line drawing tool to show how a specific tax affects the supply of minutes. Label this line ​'S1​'. Carefully follow the instructions​ above, and only draw the required objects.

-landline d curve is vertical -wireless d curve is elastic -supply moves upward horizontally D. The deadweight loss in the landline market is zero because demand is perfectly inelastic.

Initially a​ firm's wage is w=​$48 and its rental cost of capital is r=​$48. After its wage rate is halved​, how do its isocost lines​ change?

-original isocost is equal K and L - new isocost is same capital but double Labor

If a competitive firm is maximizing profits by producing some quantity of output and has decided to remain in the business in short-run, which of the following must be true at that level of output?

-p = MC -MR = MC -p ≥ AVC D) All of the above.

Which of the following characteristics of a market (such as the corn market or the automobile market) can identify the type or the structure of the market

-the number of firms in the market -the ease with which firms can enter and exit the market -the ability of firms to differentiate their product. D) All of the above.

When the isocost line is tangent to the isoquant, then

-the slope of the isocost equals the slope of the isoquant. -the firm is producing that level of output at minimum cost. -the firm is operating efficiently. D) All of the above

1. The above figure shows the cost curves for a competitive firm. If the firm is to earn some profit, price must exceed 2. The above figure shows the cost curves for a competitive firm. The firm will incur losses if the price is less than 3. The above figure shows the cost curves for a competitive firm. If the market price is $15 per unit, the firm will earn profits of

1. $10 -p must be greater than AC to earn some profit 2. $10 -if p is less than AC it will lose money 3. 160 -profit = R -C -(15 x 40) - (11 x 40) = 160

Are firmsLOADING... with limited liabilityLOADING... likely to be larger than other​ firms? ​ Why? Firms with limited liability are likely to be

A. large firms because limited liability allows firms to raise more funds.

1. In the diagram below, we have a market demand and a market supply curves. The equilibrium in this market, as you can see in the diagram, is given by p*=$60 and Q*=80. The consumer surplus at the equilibrium is equal to 2. In the diagram above, we have a market demand and a market supply curves. The equilibrium in this market, as you can see in the diagram, is given by p*=60 and Q*=80. The producer surplus at the equilibrium is equal to 3. The total welfare in a market is the sum of the consumer and producer surpluses. That is, Total Welfare =CS+PS. Based on what you found in the above two questions, what is the amount of total welfare in the above diagram? A) $2100.

1. $1600 -CS = 1/2(100-60)(80) 2. $2000 -PS= (50-10)(80) 3. 36000 -W= 1600+2000 =3600

1. The above figure shows the cost curves for a competitive firm. If the firm is to operate in the short run, price must exceed 2. The above figure shows the cost curves for a competitive firm. If the profit-maximizing level of output is 40 price is equal to

1. $5 (p>min AVC) 2. $15 (where q=40 meets MC bc MC=P)

1. The above figure shows the market demand curve for telecommunication while driving one's car (time spent on the car phone). At the current price of $0.35 per minute, consumer surplus equals 2. The above figure shows the market demand curve for telecommunication while driving one's car (time spent on the car phone). The demand curve is given by Q=1000-400p. The current price is $0.35 per minute. If the price were to increase by ten cents per minute, consumer surplus would

1. $924.50 -1/2(2.50-.35)(860) 2. fall by $84 -find new Q by plugging new p (.45) into q equation -find CS = 1/2(2.05)(820)

Under what conditions do the following production functions exhibit​ decreasing, constant, or increasing returns to​ scale? The production function 1.q=L+K 3. The production function q=L^aK^b 3. q=L + L^aK^a = K

1. always exhibits constant returns to scale. 2. exhibits increasing returns to scale if a+b>1 and decreasing returns to scale if a+b<1. 3.exhibits increasing returns to scale if a+b>1 and decreasing returns to scale if a+b<1.

1. The production function Q=2.83L^1.52K^0.82 2. The production function Q=1.38L^0.144M^0.856 3.The production function Q=L^0.23K^0.10M^0.66

1. always exhibits increasing returns to scale. 2.always exhibits constant returns to scale. 3.always exhibits decreasing returns to scale.

Under what conditions do the following production functions exhibit​ decreasing, constant, or increasing returns to​ scale? The production function q=L+K The production function q=L^aK^b The production function q=L+L^aK^b+K

1. constant 2. exhibits increasing returns to scale if a+b>1 and decreasing returns to scale if a+b<1. 3. exhibits increasing returns to scale if a+b>1 and decreasing returns to scale if a+b<1.

Assume a​ Cobb-Douglas production function of the​ form: q=10L^0.09K^0.94. What type of returns to scale does this production function​ exhibit? In this​ instance, returns to scale equal This production function exhibits

1.03 (add exponents together) increasing returns to scale.

Suppose the production function of a firm is given by € Q= LK2. The prices of labor and capital are $2 and $5, respectively. We are told that, in the short-run, capital is fixed at € K= 10. 1. Derive the formula for the total cost (that is, the cost equation) for this firm in the short-run 2. write down the formula for fixed cost and the formula for variable cost.

1.C=2L +50 -C = 2L +5(10) 2. FC = 50 VC = Q/50 -solve for L -Q=L(10)^2 -Q=100L -L=Q/100 -plug into C equation -C=2(Q/100) -C=Q/50

Assume a competitive firm faces a market price of ​$120​, a cost curve​ of: C​ = 13q3 + 20q + 500​, and a marginal cost​ of: MC = q2 +20. What is the​ firm's profit maximizing output​ level? What is the​ firm's profit maximizing​ price? What is the​ firm's profit? ​ In the​ short-run, this firm should

10 units $120 $166.7 produce

Suppose the total cost of producing T-shirts can be represented as C = 50 + 2q. The average cost of the 5th T-shirt is

12 -ATC=TC/Q -(50+2(5))/5=12

Assume a competitive firm faces a market price of ​$150​, a cost curve​ of: C​ = 13q3 + 6q + 1,500​, and a marginal cost​ of: MC = q2 +6. What is the​ firm's profit maximizing output​ level? ​ What is the​ firm's profit maximizing​ price? What is the​ firm's profit? In the​ short-run,

12 units $150 -348 this firm should produce.

Suppose the total cost of producing T-shirts can be represented as C = 50 + 2q2. The marginal cost when q=4 is

16 -MC = 4q -4(4)=16

The marginal product of labor can be determined using the total product of labor curve. Using the equation for the production​ function: q = 8LK + 5L2 − (1/3)L^3​, the level of output when L​ = 8 and K ​= 25 is

1749.33

Suppose the total cost of producing T-shirts can be represented as C = 50 + 2q. The marginal cost of the 5th T-shirt is (Hint: You have to differentiate C to find the MC formula.)

2

Under what conditions does a​ Cobb-Douglas production​ function, q=AL^aK^b​, exhibit​ decreasing, constant, or increasing returns to scale Show how output changes if both inputs are doubled. If the inputs​ double, then, as a function if​ q, a, and​ b, output increases by Give a rule for determining the returns to scale. Let g=a+b. For​ example, if g=0.63​, then the production function exhibits decreasing returns to​ scale, and doubling the inputs will increase output by

2^a+b If g=​1, then the production function exhibits constant returns to​ scale, if g<​1, then the production function exhibits decreasing returns to​ scale, and if g>​1, then the production function exhibits increasing returns to scale. 54.76 (plug 0.63 into 2^0.63 and subtract 1 to find percentage)

Ben swims​ 50,000 yards per week in his practices. Given this amount of​ training, he will swim the​ 100-yard butterfly in 55.4 seconds and place 9th in a big upcoming meet. ​ Ben's coach calculates that if Ben increases his practice to​ 60,000 yards per​ week, his time will decrease to 51.9 seconds and he will place 6th in the meet. If Ben practices​ 70,000 yards per​ week, his time will be 50.7 seconds and he will win the meet. In terms of​ Ben's time in the big​ meet, what is his marginal productivity of the number of yards he​ practices? The marginal product of increasing practice yards from​ 50,000 to​ 60,000 is _____ and the marginal product of increasing practice yards from​ 60,000 to​ 70,000 is _____

3.5 seconds; 1.2 seconds Is there diminishing marginal productivity of practice​ yards? yes.

f the inverse demand function for books is p=60−Q and the supply function isQ=p​, what is the initial​ equilibrium? What is the welfare effect of a specific tax of τ ​= ​$4​? The initial equilibrium quantity is The specific tax of τ ​= $4 creates a deadweight loss of

30 $4 (add $4 to the d function and set equal to supply function)

The marginal product of increasing practice yards from​ 50,000 to​ 60,000 is _________ place(s)​, and the marginal product of increasing practice yards from​ 60,000 to​ 70,000 is ________ place(s).

3;5 Is there diminishing marginal productivity of practice​ yards? No

Sarah earns $40,000 per year working for a large corporation. She is thinking of quitting this job to work full time in her own business. She will invest her savings of $50,000 (which currently has an annual 10% rate of return) into the business. Her annual opportunity cost of this new business is

45,000 -opportunity cost of the return rate (50,000-5,000)

Assume a competitive firm faces a market price of ​$70​, a cost curve​ of: C​ = 0.003q^3 ​+ 50q ​+ 1000​, and a marginal cost​ of: MC​ = 0.009q^2​ + 50. The​ firm's profit maximizing output level is and the per unit profit at this output level is ​ This firm will _________ in the​ short-run. The firm will realize ___________ In the​ long-run, if circumstances do not​ change, ____________

47.14 units −7.88 produce; economic loss. this firm will shut down.

If an isocost line crosses the isoquant twice, a cost minimizing firm will

A) use a different isocost line to select the bundle of inputs.

If the supply function is Q=10+p​, what is the producer surplus if price is​ 20?

A. 400

Which of the following best describes the implications of a deadweight​ loss?

A. Economic resources are not being allocated​ efficiently: either too much or not enough of the good is being produced.

Many marginal cost curves are​ U-shaped. As a​ result, it is possible that the MC curve hits the demand or price line at two output levels. Which is the profit maximizing​ output? ​ Why?

A. Profit is maximized when MC intersects demand from below because at any quantity greater than this MC is greater than marginal revenue.

Food manufacturers are usually less affected by recessions than are firms in other industries. ​ Nonetheless, during major economic​ downturns, the demand curve for food products may shift to the​ left, and firms must consider whether to reduce production by laying off some workers. To make this​ decision, firms face a managerial​ problem: How much will the output produced per worker rise or fall with each additional​ layoff? ​ Consequently, will​ productivity, as measured by the average product of labor​, rise or fall during a​ recession? For some production​ functions, layoffs always raise labor productivity because the APL curve is downward sloping everywhere. For​ example, layoffs raise the average product of labor for any​ Cobb-Douglas production​ function, q=ALαKβ​, where α is greater than zero and less than one. ​ Thus, in many U.S.​ industries, such as the food and kindred products​ industry, when workers are laid off during a​ recession, labor productivity rises. This increase in labor productivity reduces the impact of the recession on output in the United States. How would this answer change if we used the marginal product of labor rather than the average product of labor as our measure of labor​ productivity? Assume the food and kindred products industry is accurately represented with a​ Cobb-Douglas production function where α is less than one. Laying off workers will result in the marginal product of labor

A. increasing because the MPL curve must be downward sloping for the APL curve to be everywhere downward sloping.

A Chinese high technology manufacturing firm has a production function of q=9L0.20K0.80. ​(based on​ Zhang, et​ al., 2012). It faces prices of w=​$2 and r=​$8. What are its​ short-run average variable and marginal cost​ curves? Let K be fixed in the short run. The​ firm's short-run average variable cost​ curve, AVC, as a function of K and q is AVC​ = ​$ The​ firm's marginal cost​ curve, MC, as a function of K and q is MC​ =

AVC= 2Q^4/(9k^0.8)^5 -solve quantity equation for L -multiply by wage and divide by q MC= 10Q^4/(9K^0.8)^5 -take variable costs and derive in regards to Q

Consider Boeing​ (a producer of jet​ aircraft), General Mills​ (a producer of breakfast​ cereals), and Wacky​ Jack's (which claims to be the largest U.S. provider of singing​ telegrams). For which of these firms is the short run the longest period of​ time? For which is the long run the​ shortest? Explain. The short run is longest for

Boeing because aircraft production requires​ large, specialized machines and the long run is shortest for Wacky​ Jack's because providing singing telegrams requires primarily labor.

What is the​ long-run cost function for a​ fixed-proportions production function when it takes one unit of labor and two units of capital to produce one unit of​ output? Describe the long-run cost curve Multiply the inputs by their prices and sum to determine total cost. Let w be the cost of a unit of labor and r be the cost of a unit of capital. The​ long-run cost function​ C(q) for the​ fixed-proportions production function in terms of​ w, r, and q is The​ long-run cost curve is

C(q) = 1wq + 2rq straight line with a slope of ​(1w+2​r). This fixed proportions production function exhibits no economies of scale

A large city has nearly 500​ restaurants, with new ones entering regularly as the population grows. The city decides to limit the number of restaurant licenses to 500. Which characteristics of this market are consistent with perfect competition and which are​ not? Is this restaurant market likely to be nearly​ competitive? Explain your answer. Which of the following characteristics are consistent with perfect​ competition? ​(Check all that​ apply.) This market is...

C. New restaurants regularly entering. Your answer is correct. D. A market with 500 restaurants. unlikely to be nearly competitive with differentiated food.

A production function is said to be homogeneous of degree g if​ f(xL, ​xK)=xg​f(L, ​K), where x is a positive constant. That​ is, the production function has the same returns to scale for every combination of inputs. For such a production​ function, show that the marginal product of labor and the marginal product of capital functions are homogenous of degree g−1. If​ f(xL, ​xK)=xg​f(L, ​K), then the marginal product of labor is homogeneous of degree g−1 because If​ f(xL, xK)=x^g​f(L,K), then the marginal product of capital is homogeneous of degree g−1 bc

C. fL=x^(g−1)fL. A. fK=x^(g−1)fK.

If the inverse demand function for radios is p=a−bQ​, what is the consumer surplus​ (CS) if the market price is a/2​?

CS​ = a^2/8b

Consider the following​ conditions: A market with 10 identical​ firms: Market price​ = ​$20​, Each firm has a marginal cost​ (MC) of production of 2q. MC​ = 2q

Calculate the market producer​ surplus: ​$1000

Consider the inverse demand​ curve: p=80− 1Q. Assume the market price is ​$10.00. Calculate consumer surplus at the equilibrium market price and quantity. Now suppose a government imposes a tax on the good that increases the market price to ​$20.00.

Consumer surplus​ (CS) is ​$2450 Consumer surplus will decrease by ​$650

Many car owners and car dealers describe their different cars for sale in the local newspapers and list their asking price. Many people shopping for a used car consider the different choices listed in the paper. The absence of which condition prohibits this market from being described as perfectly competitive?

Consumers believe all firms sell identical products.

What is the principle distinction between explicit costs and implicit​ costs?

Explicit costs are​ direct, out-of-pocket​ payments, while implicit costs are all opportunity costs.

For a linear production​ function, q=​f(L,K)=6L+​K, what is the​ short-run production function given that capital is fixed at K=150​? The​ short-run production function​ (as a function of​ L) is The marginal product of labor is:

Q=6L+150 MPl=6

When the production function is​ linear: q​ = 0.25L​ + 0.75K, the factors are perfect substitutes for one another and the isoquant is linear. Determine the equation for the isoquant when output equals 20 units. Assuming capital is plotted on the vertical axis and labor is plotted on the horizontal​ axis, what is the marginal rate of technical substitution in this​ case?

K = 26.67 - 0.333L MRTS​ = −0.33 ​

Use the tangency ruleLOADING... to determine the​ cost-minimizing bundles of labor and capital for a general​ Cobb-Douglas production​ function, q=ALaKb​, and for the specific beer production​ function, q=1.516L0^.6K^0.4​, where w=​$24 and r=​$2. Determine the tangency condition for the general​ Cobb-Douglas production function. At the​ cost-minimizing bundle as a function of​ L, a,​ b, w, and​ r, K= Substitute in the specific values for our beer example. Part 5 At the​ cost-minimizing bundle as a function of​ L,

K=WbL/ra K=8L

Give the formulas for and plot average fixed​ cost, AFC, marginal​ cost, MC, average variable​ cost, AVC, and average​ cost, AC, if the cost function​ is: C=6+q^2.

MC=2q AFC=6/q AVC=q AC=(6+q^2)/q

Suppose the total cost of producing T-shirts can be represented as C = 50 + 2q. Which of the following statements is TRUE at all levels of production?

MC=AVC -MC=2 (derivative with respect to q) -AVC=2q/q=2

Suppose a competitive firm has​ cost, C​ = ​(0.002q^3​) ​+ (22q)​ + 750, marginal​ cost, MC​ = 0.006q^2​ + 22, and​ revenue, R​ = 80q. If the firm produces 150 units of​ output,

MR​ < MC. At this output level​ (150 units), marginal profit is negative & profit is positive. (answers B and C) The​ firm's profit maximizing level of output ​(rounded to the nearest​ integer) is 98

If the cost function for​ John's shoe repair​ is: C(q)=100+10q−q2+13q3​, and its marginal cost function​ is: MC=10−2q+q2​, which of the following​ is/are the​ profit-maximizing condition for​ John's shoe repair if the market is prefectly​ competitive?

P​ = 10−2q+q2 MR​ = 10−2q+q2 Both A and B.

What is the production function if​ labor, L, and​ capital, K, are perfect substitutes and each unit of q requires 1 unit of L or 1 unit of K​ (or a combination of these inputs that adds to 1​)? Part 2 The production function is

Q= L + K

To speed relief to isolated South Asian communities that were devastated by the December 2004​ tsunami, the U.S. government doubled the number of helicopters from 45 to 90 to deliver supplies in early 2005. Navy admiral Thomas​ Fargo, head of the U.S. Pacific​ Command, was asked if doubling the number of helicopters would​ "produce twice as much​ [relief]." He​ predicted, "Maybe pretty close to twice as​ much." Identify the outputs and inputs and describe the production process. What phenomena would result in a less than doubling of relief even though the number of helicopters was​ doubled? This economic phenomena is called

Relief is produced from donated supplies and helicopter transportation. diminishing marginal returns.

Sarah's demand curve for juice has the same slope as Pete's; however, it lies to the right of Pete's. An increase in the price of juice will cause (hint: if you draw the diagram it will be easier to answer this question)

Sarah to incur a greater loss of consumer surplus than Pete will.

Consider the market for wheat where demand is given​ by: Qd=80−2p and supply is given​ by: Qs=10 + 2p. Now suppose​ that, due to a market failure​ (an artificial shipping​ constraint), a maximum of 40.00 units of wheat can be supplied by firms in the market. ​

The amount of the deadweight loss caused by the market failure is ​$12.5

Suppose that the demand curve for wheat is QD=200−10p and the supply curve is QS=10p. The government provides producers with a specific subsidy of s=​$1 per unit. How do the equilibrium price and quantity​ change? What effect does this tax​ (subsidy) have on consumer​ surplus, producer​ surplus, government​ revenue, welfare, and deadweight​ loss?

The equilibrium price decreases by ​$0.50 and the equilibrium quantity increases by ​$5 units. ​ Consumer surplus increases by ​$51.25 Producer surplus increases by ​$51.25 Government revenue decreases by ​$105 ​Therefore, deadweight loss from the subsidy is ​$2.5

If a firm is currently in a​ short-run equilibrium earning a​ profit, what impact will a​ lump-sum tax have on its production​ decision? If a firm is currently in a​ short-run equilibrium earning a​ profit, what impact will an increase in variable factor prices have on its production​ decision?

The firm will not change output but earn a lower profit The firm will decrease output and earn a lower profit.

In the short​ run, we assume that capital is a fixed input and labor is a variable​ input, so the firm can increase output only by increasing the amount of labor it uses. In the​ short-run, the​ firm's production function is q = f(L, K)​, where q is​ output, L is​ workers, and K is the fixed number of units of capital. A specific equation for the production function is given​ by: q = 8KL+ 5L^2 − 1/3L^3. or​ , when K ​= 27​, q = (8×27×L) + 5L^2 − 1/3L^3.

The level of output q for 10 units of labor input is 2326.67 The average productivity of these 10 units of labor is 232.67 The marginal productivity of using one more unit of labor input is 210.66 ​ Given the relationship between the average productivity and the marginal​ productivity, the average productivity of labor is falling.

A U.S. electronics firm is considering moving its production abroad. Its production function is q=L0.6K0.4 ​(based on​ Hsieh, 1995), so its MPL=0.6K0.4/L0.4 and its MPK=0.4L0.6/K0.6. In the United​ States, w=​$6 and r=4. In​ Mexico, the wage is 40​% lower than in the United States but the firm faces the same cost of​ capital: ​w*=​$3.60 and ​r*=4.

US: L=100, K=100, C=1000 Mexico: L=122.67, K= 73.60, C=736.01 -set MPl/MPk = W/R -plug k into quantity equation to find L -plug l back into K equation -to find cost, multiple L by w and K by r

The marginal product is the partial first derivative of the production function with respect to​ labor: ∂q/∂L = MPL = 8K + 10L − L^2.

Using the equation for the marginal​ product, when labor is 8 units and K= 25​, the marginal product is 216 Using this same equation for the marginal​ product, when labor increases to 12 units and K=25​, the marginal product is 176​

During​ recessions, American firms lay off a larger proportion of their workers than Japanese firms do. ​ (It has been claimed that Japanese firms continue to produce at high levels and store the output or sell it at relatively low prices during the​ recession.) Would you expect the average product of labor to be higher in Japan or the United​ States? ​ Why? Assume that the production function remains unchanged over a period that is long enough to include many recessions and​ expansions, that Japanese and American firms have identical production​ functions, and that Japan and the U.S. produce using the same ratio of factors during good times.

With diminishing marginal​ returns, the average product of labor is higher in the U.S. because the marginal product of labor rises when workers are laid off.

Does​ Ben's marginal productivity of the number of yards he practices depend on how he measures his​ productivity, either place or​ time, in the big​ meet?

Yes

Should a competitive firm ever produce when it is losing​ money? Why or why​ not?

Yes, as long as revenue can cover total variable costs plus any portion of fixed costs.

You enter a store and buy a bottle of soda. Do you usually receive consumer surplus?

Yes, because you wouldn't buy the soda if your willingness to pay would be less than the price.

Joey's lawn-cutting service recently traded in its push mowers for gasoline-powered mowers. Joey still requires one worker per lawnmower; however, more grass is now cut in the same amount of time as before. This is an example of

a better technology

Which situation is most likely to exhibit diminishing marginal product to labor?

a factory that hires more workers and never increases the amount of machinery

Variable costs are

a production expense that changes with the quantity of output produced.

Fixed costs are

a production expense that does not vary with output

Suppose that the demand curve for wheat is Q=120−10p and the supply curve is Q=10p. The government imposes a price ceiling of p=$4 per unit. a. How do the equilibrium price and quantity​ change? b. What effect does this ceiling have on consumer​ surplus, producer​ surplus, and deadweight​ loss?

a. The equilibrium quantity without the price ceiling is 60 and the price without the price ceiling is ​$6. The equilibrium quantity with the price ceiling is 40 b. The change in consumer surplus​ (CS) is ​$60 The change in producer surplus​ (PS) is ​−100 ​ The deadweight loss​ (DWL) is ​$40

a. q = 3L + 2K b. q = (2L + 2K)^0.5 c. q = 3L×K^2 d. q = L^0.5 × K^0.5 e. q = 4L^0.5 + 4K

a. constant b. decreasing c. increasing d. constant e. decreasing

Economic costs of an input include

both implicit and explicit costs

If a firm manufactures in its home​ country, it faces input prices for labor and capital of w and r and produces q units of output using L units of labor and K units of capital. ​ Abroad, the wage and the cost of capital are twice as much as at home. If the firm manufactures​ abroad, will it change the amount of labor and capital it uses to produce​ q? Determine whether the change in factor prices affects the isoquant or the isocost lines. The change in factor prices will The change in factor prices will Using a rule for cost​ minimization, determine whether the firm changes its input mix. The firm will Calculate the original cost and the new cost of producing q units of output and compare them. In terms of​ w, r,​ L, and​ K, the​ firm's original cost ​(C1​) of producing q units of output was

not affect the isoquants because the production function has not changed. not affect the slope of the isocost lines because relative prices are unchanged. not change its input combination because the slopes of the isoquant and isocost lines are unchanged. C1= wL + rK C2 = 2wL + 2rK Thus, the​ firm's cost of producing q units of output doubles when the input prices double.

Joey's Lawncutting Service rents office space from Joey's dad for $300 per month. Joey's dad is thinking of increasing the rent to $400 per month. As a result, in the short run, Joey's marginal cost of cutting grass will

not change

In the short-run,

one or several inputs are fixed

he above figure shows the short-run production function for Albert's Pretzels. The marginal productivity of labor equals the average productivity of labor

only for the first worker.

Returns to scale is a concept that applies

only in the long run

If a competitive firm finds that it maximizes short-run profits by shutting down, which of the following must be true?

p < AVC for all levels of output.

If a competitive firm is maximizing profits by producing some quantity of output and has decided to remain in the business in short-run, which of the following must be true at that level of output?

p ≥ AVC.

If a firm is a price taker, then its marginal revenue will always equal

price

Dell computers has increased production efficiency over the years. This most probably means that Dell is now

producing with fewer inputs

The cost function for Acme Laundry is ​C(q)=30+10q+q^2​, where q is tons of laundry cleaned. What q should the firm choose so as to maximize its profit if the market price is​ p? The output level at which the​ firm's profit is maximized as a function of p is If p=80​, then Acme Laundry should produce ​

q = (p−10)/2 (derivative of C function) 35 units (plug into q function)

For a linear production​ function, q=​f(L,K)=2L+6​K, what is the​ short-run production function given that capital is fixed at K=250​? The​ short-run production function​ (as a function of​ L) is The marginal product of labor ​(MPL​) is

q= 2L + 1500 MPl = 2

For a linear production​ function, q=​f(L,K)=5L+8​K, what is the​ short-run production function given that capital is fixed at K=200​? The​ short-run production function​ (as a function of​ L) is q= What is the marginal product of​ labor? The marginal product of labor ​(MPL​) is

q= 5L + 1600 MPl=5

If the wage increases the isocost line will

rotate inward around the point where only capital is employed in production

If a firm operates in a perfectly competitive market, then it will most likely

settle for whatever price is offered.

If w = $10 and r = $5, what is the slope of an Isocost line?

slope of isocost= -w/r -2

Does the marginal rate of technical substitution ​(MRTS) vary along the isoquant for the firm that produced potato salad using Idaho and Maine​ potatoes? What is the MRTS at each point along the​ isoquant? Assume that Idaho and Maine potatoes are identical. Determine the shape of the isoquant The potato salad isoquants are The MRTS along the potato salad isoquant is The MRTS at each point along an isoquant is

straight lines constant -1 The marginal product of Idaho and Maine potatoes is 2 potato salads. (q increase by 12 and potatoes increase by 6, so 12/6=2)

Total Product is

the amount of output that can be produced by a given amount of labor.

Joey cuts grass during the summer. He owns one lawn mower. For him, the short run is equal to

the amount of time it takes to buy another lawn mower

The Marginal Product of Labor is

the change in total product resulting from an extra unit of labor, holding other factors constant.

The slope of an isoquant tells us

the decrease in capital necessary to keep output constant when labor increases by one unit

Producer surplus is equal to

the difference between price and marginal cost for all units sold

A firm's marginal cost can always be thought of as the change in total cost if

the firm produces one more unit of output.

The steeper an isoquant is ​(labor measured on the horizontal axis​):

the greater is the marginal productivity of labor relative to that of capital.

To say that isoquants are convex is to say​ that:

the marginal rate of technical substitution falls as labor increases and capital decreases.

Which of the following statements best describes the production function?

the maximum level of output generated from given level of inputs

The competitive firm's supply curve is equal to

the portion of its marginal cost curve that lies above AVC.

The Average Product of Labor is

the ratio of output to the number of workers used to produce that output.

A firm will shut down in the short run if

total revenue from operating would not cover variable costs.


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