econ 321 exam #2
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+2r). 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)=xgf(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)=xgf(L, K), then the marginal product of labor is homogeneous of degree g−1 because If f(xL, xK)=x^gf(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+6K, 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+8K, 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.
