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intermediate microeconomics
Study Guide For N. Gregory Mankiw's Principles Of Microeconomics 5th Edition David R. Hakes - Solutions
20.7 Pursuing the Query of Example 20.1 a bit further, calculate an explicit expression for the minimum value for S as a function of the number of firms (n) seeking tacit collusion through trigger strategies. Explain also how the maximum attainable profits (TT* < TTm)varies as a function of 8 and n
20.6 The Wave Energy Technology (WET) company has a monopoly on the production of vibratory waterbeds. Demand for these beds is relatively inelastic—at a price of $1,000 per bed, 25,000 will be sold, whereas at a price of $600, 30,000 will be sold. The only costs associated with waterbed
20.5 The world's entire supply of kryptonite is controlled by 20 people, with each having 10,000 grams of this potent mineral. The world demand for kryptonite is given by Q= 10,000- l,000P, where Pis the price per gram.a. If all owners could conspire to rig the price of kryptonite, what price would
20.4 Two firms (A and B) are considering bringing out competing brands of a healthy cigarette.Payoffs to the companies are as shown in the table (A's profits are given first):Firm B Produce Don't Produce Produce FirmA _ , _, , Don t Producea. Does this game have a Nash equilibrium?b. Does this game
20.3 In the ice cream stand example of Chapter 19, assume each stand has five possible locational strategies—locating 0, 25, 50, 75, or 100 yards from the left end of the beach.Describe the payoff matrix for this game, and explain whether it has an equilibrium strategy pair.
19.10. Suppose each firm operates under conditions of increasing marginal cost but that firm A has a larger scale of operations than does firm B in the sense that MCA < MCB for any given output level. In a Nash equilibrium, will marginal cost necessarily be equalized across the two firms? Will
20.2 Suppose the two firms in a duopoly pursue Cournot competition as described in Equation
20.1 Suppose firms A and B operate under conditions of constant average and marginal cost, but that MCA = 10, MCB = 8. The demand for the firms' output is given by QD = 500 - 20P.a. If the firms practice Bertrand competition, what will be the market price under a Nash equilibrium?b. What will the
19.9 The demand for telephones in a midsize city is given by Q= 1,000 - 50P, where Qis the number of homes buying service (in thousands) and Pis the monthly connect charge (in dollars). Phone system costs are given by TC = 500 In (AQ- 20) for Q> 200.a. Is telephone production a natural monopoly in
19.8 Suppose a firm is considering investing in research that would lead to a cost-saving innovation.Assuming the firm can retain this innovation solely for its own use, will the additional profits from the lower (marginal) costs be greater if the firm is a competitive price taker or if the firm is
19.7 Suppose demand for crude oil is given by Q= -2,000P+ 70,000, where Q 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 by MC = q + 5, where q is
19.6 S. Salop provides an instructive model of product differentiation. He asks us to conceptualize the demand for a product group as varying along a circular spectrum of characteristics(the model can also be thought of as a spatial model with consumers located around a circle). Demanders are
19.5 One way of measuring the size distribution of firms is through the use of the Herfindahl Index, which is defined as wherea, is the share of firm i in total industry revenues. Show that if all firms in the industry have constant returns«-to-scale production functions and follow Cournot output
19.4 Suppose a firm's costs for dollars spent on product differentiation (or advertising) activities(z) and quantity {q) can be written as TC = g(q) + z g'(q)>0, and that its demand function can be written as q=q{P,z).Show that the firm's profit-maximizing choices for Pand z will result in spending
19.2 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.a. Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profits.b. Suppose a second firm
19.1 Assume for simplicity that a monopolist has no costs of production and faces a demand curve given by Q= 150 -P.a. Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolist's profits.b. Suppose a second firm enters the market. Let qx be the
18.10 Suppose a monopolist produces alkaline batteries that may have various useful lifetimes(X). Suppose also that consumers' (inverse) demand depends on batteries' lifetimes and quantity (Q) purchased according to the function P(Q,X)=g(X'Q), where g' < 0. That is, consumers care only about the
18.9 Suppose the government wished to combat the undesirable allocational effects of a monopoly through the use of a subsidy.a. Why would a lump-sum subsidy not achieve the government's goal?b. Use a graphical proof to show how a per-unit-of-output subsidy might achieve the gov ernment's goal.c.
18.8 Suppose a perfectly competitive industry can produce widgets at a constant marginal cost of$10 per unit. Monopolized marginal costs rise to $12 per unit because $2 per unit must be paid to lobbyists to retain the widget producers' favored position. Suppose the market demand for widgets is
18.7 Suppose a monopoly can produce any level of output it wishes at a constant marginal (and average) cost of $5 per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the first market is given bya, = 55 - pu and the demand curve in
18.5 Suppose a monopoly market has a demand function in which quantity demanded depends not only on market price (P) but also on the amount of advertising the firm does (A, measured in dollars). The specific form of this function is Q= (20 - P)(l + 0.1A - 0.01A 2).The monopolistic firm's cost
18.4 Suppose the market for Hula Hoops is monopolized by a single firm.a. Draw the initial equilibrium for such a market.b. Now suppose 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 this
18.3 A single firm monopolizes the entire market for widgets and can produce at constant average and marginal costs of AC = MC = 10.Originally, the firm faces a market demand curve given by Q=60- P.a. Calculate the profit-maximizing price-quantity combination for the firm. What are the firm's
18.2 A monopolist faces a market demand curve given by d = 70 - P.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? What is the price at this output level? What are the monopolist's
18.1 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 — Pa. Calculate the profit-maximizing price-quantity combination for the monopolist. Also cal culate the monopolist's profits.b. What output level would be
17.10 The used car supply in Metropolis consists of 10,000 cars. The value of these cars ranges from$5,000 to $15,000, with exactly one car being worth each dollar amount between these two figures. Used car owners are always willing to sell their cars for what they are worth. Demanders of used cars
17.9 Suppose the demand curve for corn at time t is given by Qt = 100 - 2Pt and supply in period t is given by& = 70 + E(Pt), where E(Pt) is what suppliers expect the price to be in period t.a. If in equilibrium E{P,) = Pt, what are the price and quantity of corn in this market?b. Suppose suppliers
17.8 Suppose that the market demand for a particular product is given by QD= -1P+ 13 and the industry supply curve by Qs= 2P 2- 12P + 21.What are the equilibrium prices for this market? Which of these prices is stable by the Walrasian criterion?
17.6 In Example 17.5 each individual has an initial endowment of 500 units of each good.a. Express the demand for Smith and Jones for goods Xand Fas functions of Pxand Pj and their initial endowments.b. Use the demand functions from part (a) together with the observation that total de mand for each
17.5 Smith and Jones are stranded on a desert island. Each has in his possession some slices of ham (//) and cheese (C). Smith is a very choosy eater and will eat ham and cheese only in the fixed proportions of 2 slices of cheese to 1 slice of ham. His utility function is given by Us = min(H,
17.4 Suppose all of the firms in Utopia obey the Pareto conditions for efficiency except General Widget (GW). That firm has a monopoly in production of widgets and is the only hirer of widget makers in the country. Suppose the production function for widgets is Q=2L,(where L is the number of widget
17.3 In the country of Ruritania there are two regions, A and B. Two goods (Xand Y) are produced in both regions. Production functions for region A are given by YA = Y Lx and Lyare the quantity of labor devoted to Xand Yproduction, respectively. Total labor available in region A is 100 units. That
17.2 Consider an economy with just one technique available for the production of each good:Good _____________________Food________Cloth Labor per unit output 1 1 Land per unit output 2 1a. Suppose land is unlimited, but labor equals 100. Write and sketch the production possi bility frontier.b.
17.1 Suppose that Robinson Crusoe produces and consumes fish (F) and coconuts (C). Assume that during a certain period he has decided to work 200 hours and is indifferent as to whether he spends this time fishing or gathering coconuts. Robinson's production for fish is given by F= VLF and for
16.9 Return to Problem 16.6 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 -j of the value of transactions made per period.a. What will the money wage rate be in this
16.8 Use the simple two-good model of general equilibrium pricing developed in this chapter to illustrate a situation in which there will be two equilibrium price ratios by relaxing the assumption that the production possibility frontier is concave. Explain your result intuitively.
16.7 Suppose there are only three goods (X,, X2, and X3) in an economy and that the excess demand functions for X> and X3 are given by ED2 = -SPj/P, + 2PJP, - 1 ED3 = 4P2/P, - %PJPX - 2.a. Show that these functions are homogeneous of degree zero in Px, P2, and Ps.b. Use Walras' law to show that if
16.6 Suppose two individuals (Smith and Jones) each have 10 hours of labor to devote to producing either ice cream (X) or chicken soup (F). Smith's utility function is given by Us = X3Y 7, whereas Jones' is given by Uj = X 5Y 5.The individuals do not care whether they produce X or Y, and the
16.5 The country of Podunk produces only wheat and cloth, using as inputs land and labor. Both are produced by constant returns-to-scale production functions. Wheat is the relatively landintensive commodity.a. Explain, in words or with diagrams, how the price of wheat relative to cloth (p) deter
16.4 The purpose of this problem is to examine the relationship among returns to scale, factor intensity, and the shape of the production possibility frontier.Suppose there are fixed supplies of capital and labor to be allocated between the production of good X and good Y. The production function
16.3 Suppose an economy produces only two goods, X and Y. Production of good X is given by where Kx and Lx are the inputs of capital and labor devoted to X production. The production function for good Fis given by V— JS>-l/3 T 2/3 /— iv y Ajy j where KYa.nd LFare the inputs of capital and labor
16.2 Suppose the production possibility frontier for guns (X) and butter (Y) is given by X2 + 2F 2 = 900.a. Graph this frontier.b. If individuals always prefer consumption bundles in which Y= 2X, how much Xand Y will be produced?c. At the point described in part (b), what will be the KPT and hence
16.1 Suppose the production possibility frontier for cheeseburgers (C) and milkshakes (M) is given by C + 2M = 600.a. 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.
15.10 In our analysis of tariffs we assumed that the country in question faced a perfectly elastic supply curve for imports. Now assume this country faces a positively sloped supply curve for imported goods.a. Show graphically how the level of imports will be determined.b. Use your graph from part
15.9 In Example 15.3 we showed that the deadweight loss from a tariff of $500 on imported autos was approximately equal to the amount of tariff revenues collected. How would the marginal excess burden from increasing the tariff to $600 compare with the marginal tariff revenues collected? Explain
15.8 The domestic demand for portable radios is given by g= 5,000- 100P, where 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 by Q= 150P.a. What is the domestic equilibrium in the portable radio market?b.
15.7 Suppose that the government institutes a $5.50 per-film tax on the film copying industry described in Problem 15.3a. Assuming that the demand for copied films is that given in part (a) ofProblem 15.3, how will this tax affect the market equilibrium?b. How will the burden of this tax be
15.6 Suppose the government imposed a $3 tax on snuffboxes in the industry described in Problem 15.2.a. How would this tax change the market equilibrium?b. How would the burden of this tax be shared between snuffbox buyers and sellers?c. Calculate the total loss of producer surplus as a result of
15.4 Consider again the market for broccoli described in Problem 15.1.a. Suppose demand for broccoli shifted outward to Q= 1,270 -5P.What would be the new equilibrium price and quantity in this market?b. What would be the new levels of consumer and producer surplus in this market?c. Suppose the
15.3 The perfectly competitive videotape copying industry is composed of many firms that can copy five tapes per day at an average cost of $10 per tape. 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
15.2 The handmade snuffbox industry is composed of 100 identical firms, each having short-run total costs given by STC = 0.5q2 + lOq+5 and short-run marginal costs by SMC = q + 10, where q is the output of snuffboxes per day.a. What is the short-run supply curve for each snuffbox maker? What is the
15.1 Suppose that the demand for broccoli is given by d= 1,000 - 5P, where 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 by Q = 4P - 80.a. Show that the equilibrium quantity here is Q = 400. At
14.8 Suppose that the long-run total cost function for the typical mushroom producer is given by TC = wq 2 ~ lOq + 100, where q is the output of the typical firm and w represents the hourly wage rate of mushroom pickers. Suppose also that the demand for mushrooms is given by Q= - l,000P+40,000,
14.7 Suppose that the demand for stilts is given by Q= 1,500-50P and that the long-run total operating costs of each stilt-making firm in a competitive industry are given by TC = 0.5q 2- lOq.Entrepreneurial talent for stilt making is scarce. The supply curve for entrepreneurs is given by Qs =
14.6 A perfectly competitive 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(qt = 20). The minimum average cost is $10 per unit. Total market demand is given by Q= 1,500 -50P.a. What
14.5 Wheat is produced under perfectly competitive conditions. Individual wheat farmers have U-shaped, long-run average cost curves that reach a minimum average cost of $3 per bushel when 1,000 bushels are produced.a. If the market demand curve for wheat is given by QD = 2,600,000 - 200,000P, where
14.4 Suppose the demand for frisbees is given by g = 1 0 0 - 2P and the supply by Q=20 + 6P.a. What will be the equilibrium price and quantities for frisbees?b. Suppose the government levies a tax of $4 per frisbee. Now what will be the equilibrium quantity, the price consumers will pay, and the
14.3 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 by Q= 160,000 - 10,000P.a. Calculate the equilibrium price in the very short run.b. Calculate the demand schedule facing any one firm in this
14.1 Suppose there are 100 identical firms in a perfectly competitive industry. Each firm has a short-run total cost curve of the form C=3^0 9 3 + 0.2q 2 + 4q+l0.a. Calculate the firm's short-run supply curve with q as a function of market price (P).b. On the assumption that there are no
You are watching an election debate on television. A candidate says, "We need to stop the flow of foreign automobiles into our country. If we limit the importation of autos, our domestic auto production will rise and the United States will be better off."1. Is it likely that the United States will
20. Joe is a tax accountant. He receives $100 per hour doing tax returns. He can type 10,000 characters per hour into spreadsheets. He can hire an assistant who types 2,500 characters per hour into spreadsheets. Which of the following statements is true?a. Joe should not hire an assistant because
19. The opportunity cost of producing 1 metric ton of beef in Peru isa. 1/3 ton of fruit.b. 1 ton of fruit.c. 2 tons of fruit.d. 3 tons of fruit.e. 6 tons of fruit.
18. Peru will exporta. both fruit and beef.b. fruit.c. beef.d. neither fruit nor beef.
17. Argentina has a comparative advantage in the production of both fruit and beef.a. b. fruit.c. beef.d. neither fruit nor beef.
Use the production possibilities frontiers in Exhibit 4 to answer questions 17 through 19. Assume each country has the same number of workers, say 20 million, and that each axis is measured in metric tons per month.
16. Suppose the world consists of two countries-the United States and Mexico. Fur- thermore, suppose there are only two goods-food and clothing. Which of the follow- ing statements is true?a. If the United States has an absolute advantage in the production of food, then Mexico must have an absolute
15. Prices of electronics can be stated in terms of units of food. What is the range of prices of electronics for which both countries could gain from trade?a. The price must be greater than 1/5 of a unit of food but less than 1/4 of a unit of food.b. The price must be greater than 4 units of food
14. Korea shoulda. specialize in food production, export food, and import electronics.b. specialize in electronics production, export electronics, and import food.c. produce both goods because neither country has a comparative advantage.d. produce neither good because it has an absolute
13. Which of the following statements about comparative advantage is true?a. Australia has a comparative advantage in the production of food while Korea has a comparative advantage in the production of electronics.b. Korea has a comparative advantage in the production of food while Australia hasc.
12. The opportunity cost of 1 unit of food in Korea isa. 2 units of electronics.b. 1/2 of a unit of electronics.c. 4 units of electronics.d. 1/4 of a unit of electronics.
11. The opportunity cost of 1 unit of food in Australia isa. 5 units of electronics.b. 1/5 of a unit of electronics.c. 4 units of electronics.d. 1/4 of a unit of electronics.
10. The opportunity cost of 1 unit of electronics in Korea isa. 2 units of food.b. 1/2 of a unit of food. C. 4 units of food.d. 1/4 of a unit of food.
9. The opportunity cost of 1 unit of electronics in Australia isa. 5 units of food.b. 1/5 of a unit of food. C. 4 units of food.d. 1/4 of a unit of food.
8. Which of the following statements about absolute advantage is true?a. Australia has an absolute advantage in the production of food while Korea has an absolute advantage in the production of electronics.b. Korea has an absolute advantage in the production of food while Australia has an absolute
The following table shows the units of output a worker can produce per month in Australia and Korea. Use this table to answer questions 8 through 15. Australia Korea Food 20 8 Electronics 5 4
7. Suppose a country's workers can produce 4 watches per hour or 12 rings per hour. If there is no trade,a. the opportunity cost of 1 watch is 3 rings.b. the opportunity cost of 1 watch is 1/3 of a ring.c. the opportunity cost of 1 watch is 4 rings.d. the opportunity cost of 1 watch is 1/4 of a
6. Suppose a country's workers can produce 4 watches per hour or 12 rings per hour. If there is no trade,a. the domestic price of 1 ring is 3 watches.b. the domestic price of 1 ring is 1/3 of a watch.c. the domestic price of 1 ring is 4 watches.d. the domestic price of 1 ring is 1/4 of a watch.e.
5. Which of the following statements is true?a. Self-sufficiency is the road to prosperity for most countries.b. A self-sufficient country consumes outside its production possibilities frontier.c. A self-sufficient country at best can consume on its production possibilities frontier.d. Only
4. According to the principle of comparative advantage,a. b. C. countries with a comparative advantage in the production of every good need not specialize. countries should specialize in the production of goods that they enjoy consuming. countries should specialize in the production of goods for
3. Which of the following statements about trade is true?a. Unrestricted international trade benefits every person in a country equally.b. People that are skilled at all activities cannot benefit from trade.c. Trade can benefit everyone in society because it allows people to specialize in
2. If a nation has a comparative advantage in the production of a good,a. it can produce that good at a lower opportunity cost than its trading partner.b. it can produce that good using fewer resources than its trading partner.c. it can benefit by restricting imports of that good.d. it must be the
1. If a nation has an absolute advantage in the production of a good,a. it can produce that good at a lower opportunity cost than its trading partner.b. it can produce that good using fewer resources than its trading partner.c. it can benefit by restricting imports of that good.d. e. it will
15. If gains from trade are based solely on comparative advantage, and if all coun- tries have the same opportunity costs of production, then there are no gains from trade.
14. If an advanced country has an absolute advantage in the production of every- thing, it will benefit if it eliminates trade with less developed countries and becomes completely self-sufficient.
13. If Germany's productivity doubles for everything it produces, this will not al- ter its prior pattern of specialization because it has not altered its comparative advantage.
When a country removes a specific import restriction, it always benefits every worker in that country.
The gains from trade can be measured by the increase in total production that comes from specialization.
Talented people that are the best at everything have a comparative advantage in the production of everything.
9. If trade benefits one country, its trading partner must be worse off due to trade.
8. If producers have different opportunity costs of production, trade will allow them to consume outside their production possibilities frontiers.
7. If a country's workers can produce 5 hamburgers per hour or 10 bags of French fries per hour, absent trade, the price of 1 bag of fries is 2 hamburgers.
6. If a producer is self-sufficient, the production possibilities frontier is also the consumption possibilities frontier.
5. Comparative advantage is a comparison among producers based on opportunity cost.
4. Self-sufficiency is the best way to increase one's material welfare.
3. Absolute advantage is a comparison among producers based on productivity.
Comparative advantage, not absolute advantage, determines the decision to specialize in production.
IfJapan has an absolute advantage in the production ofan item, it must also have a comparative advantage in the production of that item.
6. Evaluate this statement: A technologically advanced country, which is better than its neighbor at producing everything, would be better off if it closed its borders to trade because the less productive country is a burden to the advanced country.
5. Suppose a lawyer that earns $200 per hour can also type 200 words per minute. Should the lawyer hire a secretary who can only type 50 words per minute? Why?
4. Why is a restriction of trade likely to reduce material welfare?
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