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Intermediate Microeconomics and Its Application 11th edition Walter nicholson, christopher snyder - Solutions

Sometimes it is convenient to think about the consumer’s problem in its ‘‘dual’’ form. This alternative approach asks how a person could achieve a given target level of utility at minimal cost.a. Develop a graphical argument to show that this approach will yield the same choices for this
Ms. Caffeine enjoys coffee (C) and tea (T) according to the function U(C, T) = 3C + 4T.a. What does her utility function say about her MRS of coffee for tea? What do her indifference curves look like?b. If coffee and tea cost $3 each and Ms. Caffeine has $12 to spend on these products, how much
Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the fixed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit
Frisbees are produced according to the production functionq = 2K + LWhereq = Output of Frisbees per hourK = Capital input per hourL = Labor input per houra. If K = 10, how much L is needed to produce 100 Frisbees per hour?b. If K = 25, how much L is needed to produce 100 Frisbees per hour?c. Graph
Digging clams by hand in Sunset Bay requires only labor input. The total number of clams obtained per hour (q) is given byq = 100 √LWhere L is labor input per hour.a. Graph the relationship between q and L.b. What is the average productivity of labor (output per unit of labor input) in Sunset
Suppose that the hourly output of chili at a barbecue (q, measured in pounds) is characterized byq = 20√KLWhere K is the number of large pots used each hour and L is the number of worker hours employed.a. Graph the q = 2,000 pounds per hour is oquant.b. The point K = 100, L = 100 is one point on
Grapes must be harvested by hand. Fixed proportions characterize this production function—each worker must have one pair of stem clippers to produce any output. A skilled worker with clippers can harvest 50 pounds of grapes per hour.a. Sketch the grape production is oquants for q = 500, q =
Power Goat Lawn Company uses two sizes of mowers to cut lawns. The smaller mowers have a 24- inch blade and are used on lawns with many trees and obstacles. The larger mowers are exactly twice as big as the smaller mowers and are used on open lawns where maneuverability is not so difficult. The two
The production functionq = Ka LbWhere 0 ≤ a, b ≤ 1 is called a Cobb-Douglas production function. This function is widely used in economic research. Using the function, show the following:a. The production function in Equation is a special case of the Cobb-Douglas.Hamburgers per hour = q = 10
For the Cobb-Douglas production function in Problem 6.7, it can be shown (using calculus) thatMPK = aKa-1 LbMPL = bKa Lb-1If the Cobb-Douglas exhibits constant returns to scale (a þ b ¼ 1), show thata. Both marginal productivities are diminishing.b. The RTS for this function is given byRTS =
The production function for puffed rice is given byq = 100 √ KLWhere q is the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour.a. Calculate the q = 1,000 is oquant for this production function and show it on a
One-way economists measure total factor productivity is to use a Cobb-Douglas production function of the form q = A (t) KaL1-a, where A (t) is a term representing technical change and a is a positive fraction representing the relative importance of capital input.a. Describe why this production
A widget manufacturer has an infinitely substitutable production function of the formq = 2K + La. Graph the is oquant maps for q = 20, q = 40, and q = 60. What is the RTS along these is oquants?b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination
Suppose that the Acme Gumball Company has a fixed proportions production function that requires it to use two gumball presses and one worker to produce 1000 gumballs per hour.a. Explain why the cost per hour of producing 1000 gumballs is 2v + w (where v is the hourly rent for gumball presses and w
The long-run total cost function for a firm producing skateboards isTC = q3 – 40q2 + 430qWhere q is the number of skateboards per week.a. What is the general shape of this total cost function?b. Calculate the average cost function for skateboards. What shape does the graph of this function have?
Trapper Joe, the fur trader, has found that his production function in acquiring pelts is given by:q = 2 √HWhere q = the number of pelts acquired in a day, and H = the number of hours Joe’s employees spend hunting and trapping in one day. Joe pays his employees $8 an hour.a. Calculate Joe is
A firm producing hockey sticks has a production function given byq = 2 √K ∙ LIn the short run, the firm’s amount of capital equipment is fixed at K = 100. The rental rate for K is v = $1, and the wage rate for L is w = $4.a. Calculate the firm’s short-run total cost function. Calculate the
Returning to the gumball producer in Problem, let us look at the possibility that producing these delectable treats does not necessarily experience constant returns to scale.a. In Problem, we showed that the cost function for gumballs was given by TC = q (2v + w), where q is output of gumballs (in
Venture capitalist Sarah purchases two firms to produce widgets. Each firm produces identical products and each has a production function given byqi = √ Ki ∙ LiWherei = 1, 2The firms differ, however, in the amount of capital equipment each has. In particular, firm 1 has K1 = 25, whereas firm 2
In Problem we introduced the Cobb-Douglas production function of the form q = Ka Lb. The cost function that can be derived from this production function is: TC = Bq1/(a+b)va/(a+b)wb/(a+b), where B is a constant, and v and w are the costs of K and L, respectively.a. To understand this function,
In the numerical example of Hamburger Heaven’s production function in Chapter 6, we examined the consequences of the invention of a self-flipping burger that changed the production function toq = 20√KLa. Assuming this shift does not change the cost minimizing expansion path (which requires K =
In our numerical example, Hamburger Heaven€™s expansion path requires K = L because w (the wage) and v (the rental rate of grills) are equal. More generally, for this type of production function, it can be shown thatK/L = w/vfor cost minimization. Hence, relative input usage is determined
Beth’s Lawn Mowing Service is a small business that acts as a price taker (MR = P). The prevailing market price of lawn mowing is $20 per acre. Although Beth can use the family mower for free (but Problem), she has other costs given byTotal cost = 0.1q2 + 10q + 50Marginal cost = 0.2q + 10Where q
Consider again the profit-maximizing decision of Beth’s Lawn Mowing Service from Problem. Suppose Beth’s greedy father decides to charge for the use of the family lawn mower. a. If the lawn mower charge is set at $100 per week, how will this affect the acres of lawns Beth chooses to mow? What
A number of additional conclusions can be drawn from the fact that the marginal revenue curve associated with a linear demand curve is also linear and has the same intercept and twice the slope of the original demand curve.a. Show that the horizontal intercept of the marginal revenue curve (for a
Suppose that a firm faces a demand curve that has a constant elasticity of – 2. This demand curve is given byq = 256 / P2Suppose also that the firm has a marginal cost curve of the formMC = 0:001qa. Graph these demand and marginal cost curves.b. Calculate the marginal revenue curve associated
Although we only discussed profit maximization as a goal of firms in this chapter, many of the tools developed can be used to illustrate other goals as well. To do so, assume a firm faces a downward-sloping, linear demand curve and has constant average and marginal costs.a. Suppose this firm wished
A local pizza shop has hired a consultant to help it compete with national chains in the area. Because these national chains handle most business, the local shop operates as a price taker. Using historical data on costs, the consultant finds that short-run total costs each day are given by STC = 10
The town where Beth’s Lawn Mowing Service is located is subject to sporadic droughts and monsoons. During periods of drought, the price for mowing lawns drops to $15 per acre, whereas during monsoons, it rises to $25 per acre.a. How will Beth react to these changing prices?b. Suppose that weeks
In order to break the hold of Beth’s greedy father over his struggling daughter the government is thinking of instituting an income subsidy plan for the lass. Two plans are under consideration:(1) A flat grant of $200 per week to Beth,(2) A grant of $4 per acre mowed.a. Which of these plans will
Suppose the production function for high-quality brandy is given byq = √K ∙ LWhere q is the output of brandy per week and L is labor hours per week. In the short run, K is fixed at 100, so the short-run production function isq = 10 √La. If capital rents for $10 and wages are $5 per hour, show
Abby is the sole owner of a nail salon. Her costs for a manicure are given byTC = 10 + q2AC = 10/q + qMC = 2qThe nail salon is open only 2 days a week—Wednesdays and Saturdays. On both days, Abby acts as a price taker, but price is much higher on the weekend. Specifically, P = 10 on Wednesdays
Suppose the daily demand curve for flounder at Cape May is given by QD = 1,600 - 600P, where QD is demand in pounds per day and P is price per pound.a. If fishing boats land 1,000 pounds one day, what will the price be?b. If the catch were to fall to 400 pounds, what would the price be?c. Suppose
A perfectly competitive market has 1,000 firms. In the very short run, each of the firms has a fixed supply of 100 units. The market demand is given byQ = 160,000 – 10,000Pa. Calculate the equilibrium price in the very short run.b. Calculate the demand schedule facing any one firm in the
Suppose there are 100 identical firms in the perfectly competitive note card industry. Each firm has a short-run total cost curve of the form:STC = 1/300 q3 + 0.2q2 + 4q + 10and marginal cost is given bySMC = .01q2 + .4q + 4a. Calculate the firm’s short-run supply curve with q (the number of
Suppose there are 1,000 identical firms producing diamonds and that the short-run total cost curve for each firm is given bySTC = q2 + wqand short-run marginal cost is given bySMC = 2q + wwhere q is the firm’s output level and w is the wage rate of diamond cutters.a. If w = 10, what will be the
A perfectly competitive painted necktie industry has a large number of potential entrants. Each firm has an identical cost structure such that long-run average cost is minimized at an output of 20 units (qi = 20). The minimum average cost is $10 per unit. Total market demand is given byQ = 1,500
Suppose that the demand for broccoli is given byDemand: Q = 1,000 – 5Pwhere Q is quantity per year measured in hundreds of bushels and P is price in dollars per hundred bushels. The long-run supply curve for broccoli is given bySupply: Q = 4P – 80a. Show that the equilibrium quantity here is Q
The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given bySTC = 0.5q2 + 10q + 5and short-run marginal costs given bySMC = q + 10Where q is the output of snuffboxes per day.a. What is the short-run supply curve for each snuffbox maker? What is the
The perfectly competitive DVD copying industry is composed of many firms who can copy five DVDs per day at an average cost of $10 per DVD. Each firm must also pay a royalty to film studios, and the per-film royalty rate (r) is an increasing function of total industry output (Q) given byr = .002Qa.
The domestic demand for portable radios is given byDemand: Q = 5,000 – 100Pwhere price P is measured in dollars and quantity Q is measured in thousands of radios per year. The domestic supply curve for radios is given bySupply: Q = 150Pa. What is the domestic equilibrium in the portable radio
Suppose the production possibility frontier for cheeseburgers (C) and milkshakes (M) is given byC + 2M = 600a. Graph this function.b. Assuming that people prefer to eat two cheeseburgers with every milkshake, how much of each product will be produced? Indicate this point on your graph.c. Given that
Consider an economy with just one technique available for the production of each good, food and cloth:a. Supposing land is unlimited but labor equals 100, write and sketch the production possibility frontier.b. Supposing labor is unlimited but land equals 150, write and sketch the production
Suppose the production possibility frontier for guns (X) and butter (Y) is given byX2 + 2Y2 = 900a. Graph this frontier.b. If individuals always prefer consumption bundles in which Y = 2X, how much X and Y will be produced?c. At the point described in part b, what will be the slope of the
Robinson Crusoe obtains utility from the quantity of fish he consumes in one day (F), the quantity of coconuts he consumes that day (C), and the hours of leisure time he has during the day (H) according to the utility function:Utility = F1/4C1/4H1/2Robinson’s production of fish is given byF =
Suppose two individuals (Smith and Jones) each have 10 hours of labor to devote to producing either ice cream (X) or chicken soup (Y). Smith’s demand for X and Y is given byXS = 0:3/S /PXYS = 0:7/S /PYWhereas Jones’s demands are given byXJ = 0:5/J /PXYJ = 0:5/J /PYWhere IS and IJ represent
In the country of Ruritania there are two regions, A and B. Two goods (X and Y) are produced in both regions. Production functions for region A are given byXA = √LXYA = √LYLX and LY are the quantity of labor devoted to X and Y production, respectively. Total labor available in region A is 100
There are 200 pounds of food on an island that must be allocated between 2 marooned sailors. The utility function of the first sailor is given byUtility = √F1Where F1 is the quantity of food consumed by the first sailor. For the second sailor, utility (as a function of food consumption) is given
Return to Problem 10.5 and now assume that Smith and Jones conduct their exchanges in paper money. The total supply of such money is $60 and each individual wishes to hold a stock of money equal to ¼ of the value of transactions made per period.a. What will the money wage rate be in this model?
The Edgeworth box diagram can also be used to show how a production possibility frontier is constructed for an economy as a whole. Suppose there are only two goods that might be produced (X and Y), each using two inputs, capital (K) and labor (L). In order to construct the X-Y production
Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportions of 2 slices of cheese to each slice of ham. Her utility function is given by US = Min (10H, 5C). Jones, on the other
A monopolist can produce at constant average and marginal costs of AC = MC = 5. The firm faces a market demand curve given by Q = 53 – P. The monopolist’s marginal revenue curve is given by MR = 53 – 2Q.a. Calculate the profit-maximizing price-quantity combination for the monopolist. Also
A monopolist faces a market demand curve given byQ = 70 – P:The monopolist’s marginal revenue function is given byMR = 70 – 2Q:a. If the monopolist can produce at constant average and marginal costs of AC = MC = 6, what output level will the monopolist choose in order to maximize profits?
A single firm monopolizes the entire market for Batman masks and can produce at constant average and marginal costs ofAC = MC = 10.Originally, the firm faces a market demand curve given byQ = 60 – Pand a marginal revenue function given byMR = 60 – 2Qa. Calculate the profit-maximizing
Suppose that the market for hula-hoops is monopolized by a single firm.a. Draw the initial equilibrium for such a market.b. Suppose now that the demand for hula-hoops shifts outward slightly. Show that, in general (contrary to the competitive case), it will not be possible to predict the effect of
Suppose a company has a monopoly on a game called Monopoly and faces a demand curve given byQT = 100 – Pand a marginal revenue function given byMR = 100 – 2QTWhere QT equals the combined total number of games produced per hour in the company’s two factories (QT = q1 + q2). If factory 1 has a
Suppose a textbook monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per book. Assume that the monopoly sells its books in two different markets that are separated by some distance. The demand curve in the first market is given byQ1 = 55 – P1and
Suppose a perfectly competitive industry can produce Roman candles at a constant marginal cost of $10 per unit. Once the industry is monopolized, marginal costs rise to $12 per unit because $2 per unit must be paid to politicians to ensure that only this firm receives a Roman candle license.
Consider the following possible schemes for taxing a monopoly:i. A proportional tax on profitsii. A tax on each unit producediii. A proportional tax on the gap between price and marginal costa. Explain how each of these taxes would affect the monopolist’s profit-maximizing output choice. Would
Bruce runs the only bar in town. An individual consumer’s demand for bar drinks is Q = 8 – P. The associated marginal revenue curve for this consumer is MR = 8 – 2Q. The bar’s marginal cost is $2 per drink.a. Compute the profit-maximizing monopoly quantity, price, and profit from serving
Because of the huge fixed cost of running pipes to everyone’s home, natural gas is a natural monopoly. Suppose demand is Q = 100 – P and marginal revenue is MR = 100 –2Q. Suppose marginal cost is $20, and the fixed cost of setting up the natural gas pipelines is $1,000.a. Compute the industry
The pricing game between two firms, which can each set either a low or a high price, is given by the following normal form.a. Find the Nash equilibrium or equilibria of the game.b. How would you label the actions to make this a quantity game likeCournot?
Refer to Figure. Suppose demand isQ = 10,000 €“ 1,000Pand marginal cost is constant at MC = 6. From the given demand curve, one can compute the following marginal revenue curve:MR = 10 €“ Q/500a. Graph the demand, marginal cost, and marginal revenue curves.b. Calculate the price
Return to the example used in the text for the Cournot model, where demand was equal to Q = 120 – PSuppose that instead of costless production, marginal and average costs are constant at MC = AC = 30Compute the Nash equilibrium quantities, prices, and profits.
Consider the model of Bertrand competition with differentiated products from the text. Let the demand curves for firms A and B be given by Equation 12.10 and Equation 12.11, and let the firms' marginal costs be constant, given by cA and cB. It can be shown that the best-response function for firm A
Suppose firms A and B operate under conditions of constant marginal and average cost but that MCA = 10 and MCB = 8. The demand for the firms' output is given byQ = 500 – 20P.a. If the firms practice Bertrand competition, what will the Nash-equilibrium market price be? (It may help to assume that
Consider the example of the Stackelberg model discussed in the text. Firms choose quantities, with firm A moving first, and then firm B. As in the text, market demand is given byQ 120 €“ Pand production is costless.a. Recall that firm B's best-response function isqB = 120 €“
Using Equation 12.15 from the text, graph the relationship between the number of firms in the market, N, and probability, g, that the game continues from one period to the next, needed to sustain collusion in an indefinitely repeated game. What is the greatest number of firms for which collusion
Consider a two-period model with two firms, A and B. In the first period, they simultaneously choose one of two actions, Enter or do not enter. Entry requires the expenditure of a fixed entry cost of 10. In the second period, whichever firms enter play a pricing game as follows. If no firm enters,
The text mentioned a model of predatory pricing in which an incumbent tries to ''beat up'' a rival, exhausting the resources the rival needs to continue operating in the market, causing it to exit. Consider a specific example of this sort of model given by the extensive form in Figure. As the
Suppose that the total market demand for crude oil is given byQD = 70,000 – 2,000PWhere QD is the quantity of oil in thousands of barrels per year and P is the dollar price per barrel. Suppose also that there are 1,000 identical small producers of crude oil, each with marginal costs given byMC =
A landowner has three farms (A, B, and C) of differing fertility. The levels of output for the three farms with one, two, and three laborers employed are as follows:For example, if one laborer were hired for each farm, the total output would be 10 + 8 + 5 = 23. This would represent a poor
Assume that the quantity of envelopes licked per hour by Sticky Gums, Inc., is q = 10,000 √L where L is the number of laborers hired per hour by the firm. Assume further that the envelope-licking business is perfectly competitive with a market price of $0.01 per envelope. The marginal product of
Suppose there are a fixed number of 1,000 identical firms in the perfectly competitive concrete pipe industry. Each firm produces the same fraction of total market output and each firm's production function for pipe is given byq = √KLand for this production functionRTS (L for K) = K/LSuppose also
Suppose the demand for labor is given byL = – 50w + 450and the supply is given byL = 100wWhere L represents the number of people employed and w is the real wage rate per hour.a. What will be the equilibrium levels for w and L in this market?b. Suppose the government wishes to raise the
Assume that the market for rental cars for business purposes is perfectly competitive, with the demand for this capital input given byK = 1,500 – 25vand the supply given byK = 75v – 500Where K represents the number of cars rented by firms and v is the rental rate per day.a. What will be the
Suppose that the supply curve for the labor to a firm is given byL = 100wand the marginal expense of labor curve is given byMEL = L/50Where w is the market wage. Suppose also that the firm's demand for labor (marginal revenue product) curve is given byL = 1,000 – 100MRPLa. If the firm acts as a
Carl the clothier owns a large garment factory on a remote island. Carl's factory is the only source of employment for most of the islanders, and thus Carl acts as a monopsonist. The supply curve for garment workers is given byL = 80wand the marginal-expense-of-labor curve is given byMEL =
The Ajax Coal Company is the only employer in its area. It can hire any number of female workers or male workers it wishes. The supply curve for women is given byLf = 100wfMEf = Lf =50and for men byLm = 9w2mMEm = 1 / 2 √LMWhere wf and wm are, respectively, the hourly wage rate paid to female and
Mrs. Smith has a guaranteed income of $10 per day from an inheritance. Her preferences require her always to spend half her potential income on leisure (H) and consumption (C).a. What is Mrs. Smith's budget constraint in this situation?b. How many hours will Mrs. Smith devote to work and to leisure
The budget constraint facing an individual planning his or her consumption over two periods is an intertemporal one in which the present value of consumption expenditures must equal the present value of incomes in the two periods:C0 + C1/(1 + r) = Y0 + Y1(1 + r)Where Y and C represent income and
Flexible Felix views present and future consumption as perfect substitutes. He does, however, discount future consumption by a bit to reflect the uncertainties of his life. His utility function is therefore given byU (C0, C1) = C0 + C1 / (1 + δ)Where δ (which is a small positive number) is the
Two roommates, Prudence and Glitter, graduate from college and get identical jobs that pay them $50,000 this year and $55,000 next year. The roommates have different utility functions so that the marginal rates of substitution are given byMRS for Prudence = C1/3C0MRS for Glitter = 3C1/C0Assume that
The Robotics Corporation produces cuddly toys using only computer-driven robots. The quantity of toys (T) produced per year is given by T = 10√R where R is the number of robots used during each year of production.a. If the market price of robots is $2,000, the real interest rate is 0.05, and the
Acme Landfill Company is considering the purchase of 10 better trash collection trucks. Each truck costs $50,000 and will last 7 years. The firm estimates that the purchase will increase its annual revenues by $100,000 per year for as long as the trucks last. If the real interest rate is 10
Scotch whisky increases in value as it ages, at least up to a point. For any period of time, t, the value of a barrel is given by V = 100t – 6t2. This function implies that the proportional rate of growth of the value of the scotch is (100 – 12t)/V.a. Graph this scotch value function.b. At what
To calculate scarcity costs for any finite resource, a price at some future date must be assumed. Suppose, for example, that the real price of platinum will be $4,000 per ounce in 25 years.a. If the real interest rate is 5 percent and no change is expected in the real costs of producing platinum
A persistent life insurance sales man makes the following pitch: ''At your age (40), a $100,000 whole life policy is a much better buy than a term policy. The whole life policy requires you to pay $2,000 per year for the next 4 years but nothing after that. A term policy will cost you $400 per year
A car sales man once made the following pitch to one of your authors: ''If you buy this $10,000 car with cash, you will lose at least $1,500 over the next 3 years in forgone interest (assumed to be 5 percent per year). If you take one of our low-cost auto loans, you only have to pay $315 per month
Although perpetual bonds are illegal in the United States, sometimes it is easiest to assume that interest payments last forever to show some simple results based on Equation. Use that equation to show the following:$X = $1/ ia. Assuming no inflation, the value of a bond that pays $10 per year is
Draw the following incentive contracts on the same graph, with gross profit (revenue minus costs for all inputs, not including payments to the manager) for the firm on the horizontal axis and manager pay on the vertical axis as in Figure Draw a second graph with the marginal pay implied by each
Clare manages a piano store. Her utility function is given byUtility = w – 100Where w is the total of all monetary payments to her and 100 represents the cost to her of the effort of running the store. Clare's next best alternative to managing the store provides her with zero utility. The store's
Return to problem 15.2. Suppose that Clare can still choose to exert effort, as in the previous problem, but that she can also choose not to exert effort. If she does not exert effort, she has no effort cost, so her utility is just the wage, w; the shop's return is $400 for certain.a. If
Ahab's Coffee has 150 customers. Fifty of them are small and 100 are big, with appetites for coffee matching their size. Small people value coffee at $0.10 per ounce for the first 8 ounces and nothing for more than that. Large people value coffee at $0.15 cents per ounce for the first 10 ounces and
L. L. Bean, among other stores, has a policy of replacing shoes that wear out with new ones. Suppose there are two types of shoe buyers. Half of them have desk jobs and only have a 20 percent chance of wearing out their shoes. The other half has active jobs (construction, nursing) and has a 60
Tess and Meg are the only two bidders in an auction for a van Gogh painting. Each can be one of two types with equal probability: a low-value consumer with valuation $1 million or a high-value consumer with valuation $2 million. Each knows her own type but only knows the probabilities of the
Suppose 100 cars will be offered on the used-car market, 50 of them good cars, each worth $10,000 to a buyer, and 50 of them lemons, each worth $2,000.a. Compute a buyer's maximum willingness to pay for a car if he or she cannot observe the car's type.b. Suppose that there are enough buyers that
A firm earns gross profit (profit not including the wage) of 100 from a low-ability worker and 200 from a high-ability worker. A quarter of the workers are low-ability and the rest are high-ability.a. If competitive firms have no signals available, what is the equilibrium wage they would pay?b.
An incumbent firm may be a low-cost type, with constant marginal cost of production 10, or a high-cost type, with marginal cost of production 20, with probabilities t and 1 – t, respectively. The incumbent's type is private information. The incumbent produces as a monopolist in the first period.

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