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Artificial Intelligence For Games 2nd Edition Ian Millington, John Funge, Millington - Solutions
(c) Show that the profit maximizing rule for output allocation between the plants is satisfied.
(b) Use the profit maximizing rule to determine the output produced at each of the two plants and, hence, the total output of the firm.
(a) State the profit maximizing rule that determines how much output the monopoly will produce at each plant.
1 Consider a multiplant monopoly facing demand given by:The firm operates two plants with total cost functions given by:
(d) The Cairns Group includes countries like Australia and Canada which export agricultural products but have very limited domestic support programs for producers of agricultural products. Considering the strategic effects of the export subsidies by the US and the EU, what do you expect would be
(c) Now consider a country which imports agricultural products from the US or the EU. What are the terms of trade and volume of trade effects of these export subsidies in this importing country?
(b) What are the terms of trade and volume of trade effects of such an export subsidy in the United States or the EU?
(a) Use a graph like Figure 12.1 to describe the effects of an export subsidy on a country which exports agricultural products.
5 The US and EU both use export subsidies to support producers in their agriculture sectors.
4 Australia and New Zealand entered into the “Closer Economic Relations(CER) Trade Agreement” on January 1, 1983. Given your understanding of PTAs and Game Theory, try to describe the Agreement between Australia and New Zealand as a Game. Who are the players? What are the strategies and payoffs
(c) Do these tariff data support or contradict your answer to part (a)?What effect would a reduction in the tariff on imported chickens have on the price of chickens in Canada? Use a graph to answer this question, if necessary.
(b) The Uruguay Round included Articles which explicitly prohibited supply management programs. As a result, these countries were required to replace the import restrictions implied by Marketing Boards with tariffs, such as listed by Canada in the following table:Commodity WTO tariff equivalents
(a) Given discussions of entry and exit problems in Chapter 10, discuss whether these Marketing Boards provide a barrier to entry. If so, what effect would this have on the structure of competition in the primary agricultural markets in Australia, Canada, and South Korea?
3 Until recently, some countries including Australia, Canada, and South Korea used supply management programs to control production and pricing in a number of agricultural sectors. Marketing Boards in these sectors controlled production and distribution of primary agricultural products like chicken
government tariff revenue
surplus of Canadian wine producers
welfare of Canadian wine consumers
the price of wine in Canada
Canadian wine production
the volume of wine imports
(b) Suppose that the government removed the tariff on imported wine.What would happen to:
(a) Using a graph like Figure 12.1, illustrate this initial trading equilibrium in the Canadian wine market using the Canadian demand and supply curves for wine.
2 Suppose that the world price of wine pwine = $10 per bottle, and that Canada is a net importer of wine. To promote and protect wine production in the Niagara peninsula, suppose that the Canadian government charges a 20 percent tariff on wine imports.
(d) If e rises from e = 1 to ẽ = 1.5, is Home better off or worse off? Is this an improvement or a deterioration in Home’s terms of trade?
(c) If the terms of trade are e = Pguns/Proses = 1, are there gains from trade? What will be the pattern of trade?
(b) Which country has the comparative advantage in rose production, and gun production?
(a) Which country has the absolute advantage rose production, and gun production?
1 The following table shows the unit labor requirements for two commodities in two countries, Home and Foreign.
(g) List the key assumptions made in the above analysis.
(f) Which scheme will the high-cost firm prefer? Which scheme will the low-cost firm prefer? Which of the above three schemes is most efficient from the point of view of society as a whole? (Remember that the total amount of pollution is the same in all three cases.)
(e) How much does each firm spend on pollution abatement? What are the total resources spent on pollution abatement? What are the total costs of the permit mechanism to each firm?
(d) Another option for the government is to give each firm a number of pollution “permits” such that the total number of permits equals the desired amount of pollution, 104, and then let the two firms trade the permits between one another. Suppose the government allocates each firm 52 pollution
(c) What are the tax payments of each firm? How much does each firm spend on pollution abatement? What are the total resources spent on pollution abatement? What are the total costs of the tax scheme to each firm?
(b) Suppose the government decides to cut the total amount of pollution by 48 percent using a per-unit tax on pollution output.What level of the pollution tax will result in a decrease in total emissions by 48 percent?
(a) Suppose the government decides to cut the total amount of pollution by 48 percent. One way to do this is to require each firm to cut pollution by 48 percent. Calculate the amount each firm spends on pollution abatement under this plan. Calculate the total resources spent on pollution abatement,
4 Suppose a country has two firms, each engaged in different industries.Suppose that the marginal cost of pollution reduction (MCR) at one firm is given by:where QR is the amount of reduced pollution, and the marginal cost of pollution reduction at the other firm is given by:Note that the firm with
(d) Does the tax have the desired effect? If not, what change would you suggest? Explain.
(c) In an attempt to induce the firm to produce the socially optimal output level, the government imposes an effluent fee on the firm of $5 per unit of newsprint produced. Calculate the firm’s output after implementation of the scheme.
(b) Determine the marginal social cost of the firm’s newsprint manufacturing. Calculate the socially optimal output of newsprint from this firm.
(a) Determine the output of the newsprint firm.
3 A newsprint company has (private) marginal costs given by:Assume that the price of newsprint is determined, in a competitive market, to be $20 per unit. A by-product of the newsprint manufacturing process is sludge, which is dumped into a river. Suppose the costs of the sludge-dumping are
(d) Determine the price if the firm were required by regulation to charge a price equal to average cost. What problems do you think an average cost pricing scheme will encounter?
(c) If the marginal cost pricing rule is brought into effect, will the monopolist continue business or will it leave the industry? Explain.
(b) Determine the average cost curve of the monopoly. Calculate the profit per unit and the total profit for the unregulated monopolist.Calculate the profit per unit and the total profit for the monopolist under the marginal cost pricing rule.
(a) Calculate the equilibrium price and output level of the monopolist.
2 Let the inverse demand curve for a monopoly firm be:and let the total cost of the firm be:
(c) Make a rough sketch of the demand curve and the marginal cost curve of the monopolist. Indicate on the diagram: (i) the output level produced by the unregulated monopolist; (ii) the socially optimal output level; and (iii) the efficiency loss associated with the output level produced by the
Calculate the socially optimal output level. Calculate the price that government regulators will have to set under the marginal cost pricing rule in order to induce the monopolist to produce the socially optimal output level.
(b) Suppose government regulators decide to use marginal cost pricing to induce the monopolist to produce the socially optimal output level.
(a) Calculate the equilibrium price and output level of the monopolist.
Discuss the differences between these two versions of the strategic effect of the incumbent’s investment strategy. In each case, whose profits is the incumbent interested in? If firms are competing in prices, is this strategic effect positive or negative?
accommodates entry
deters entry
4 Identify the strategic effect of an incumbent firm’s investment strategy from Section 10.3 when the incumbent:
(c) An optometrist installs an in-house facility to make glasses to fit a prescription while-you-wait.In each case, discuss whether the firm is following a top dog, puppy dog, lean-and-hungry look, or fat cat investment strategy. Is the strategic effect of the firm’s investment strategy likely to
(b) A clothing outlet sells only last season’s fashions at bargain basement prices.
(a) A maker of ski boots and bindings designs a new ski boot to be used only with its own bindings, with increased safety properties.
3 Consider the following examples:
(c) Now suppose F = 25. Repeat parts (a) and (b). Would the incumbent want to follow the same strategy as in part (b)? Relate your answer to the cost of entry deterrence.
(b) Now suppose the incumbent deters entry. Solve for market price, and output and profits of each firm. Would the incumbent firm rather accommodate or deter entry? Explain your answer.
(a) Suppose marginal cost c = 5, and fixed cost F = 100. Solve for the equilibrium market price, each firm’s level of output, and equilibrium profits for both firms, when the incumbent accommodates entry.
2 In Section 10.1.2, we showed that when the market demand function was given by p = 120 − (K1 + K2), the incumbent firm deterred entry by producing the level of output and earned profits π1d given by:If the incumbent accommodated entry, the incumbent earned profits in the Stackelberg
(c) Can you interpret the fixed cost F as a cost of entry deterrence? Is the incumbent more or less likely to deter entry as F gets larger?
(b) For which values of the fixed cost F will the incumbent deter entry?
1 In Section 10.1, we showed that when the incumbent firm 1 accommodated entry, it earned profits:When this same firm chose capacity to deter entry, it earned profits:The incumbent will deter entry as long as or as long as Suppose marginal cost c=60.(a) Solve for
(c) Many retailers who include warranties with the products they sell also offer extended warranties which consumers can purchase at an extra cost. What type of information problem would an extended warranty be designed to correct?
(b) If a consumer would never buy a retailer’s product more than once, what would happen to the retailer’s incentive to offer a warranty?Would your answer change if consumers could find out about the quality of a retailer’s product before purchase?
(a) What sorts of informational asymmetries exist between buyers and sellers which would motivate retailers to offer warranties? Are these moral hazard or adverse selection problems?
4 Many retailers offer warranties on the goods they sell, whether they be electronic products (computers, stereo components), white goods(washing machines and fridges), or cars.
(e) Suppose a group of local wine producers formed a Wine Growers Association which published a monthly wine magazine which was distributed to consumers free-of-charge. If you were a wine producer, would you want to be a member of this Association? Would the existence of this Association and its
(d) How important is the cost of wine magazines or wine appreciation courses? Would you change your answers to parts 3b and 3c if the government subsidized wine appreciation courses?
(c) Would a producer want to produce a higher-quality wine if more wine magazines were published or more wine appreciation courses were offered.
(b) Discuss the wine producer’s incentive to produce a high-quality wine as a function of the number of wine experts in the economy.
(a) Does an informational asymmetry exist between wine producers and this wine consumer? What type of information problem exists?
3 Suppose a consumer is initially unaware of the quality of wine. As we discussed in this chapter, the consumer could use price as a signal of the quality of wine. But another option would be to do some research into different types of wine, by reading magazines about wine, or taking a wine
2 What would happen to the consumer’s perception of quality if BMW started producing a pick-up truck which sold for the same price as comparable trucks produced by Ford, General Motors, or Chrysler? What might you expect to happen to sales of BMW’s sedans and sports cars, if BMW did not change
(d) Would you expect a Law School which did not require an LSAT score as an admission requirement to be a higher- or lower-quality School?
(c) Short of asking an applicant whether they took a Preparation Class, can you think of anything that a Law School can do to resolve the information problem in question 1b?
(b) There exist many LSAT Preparation Classes in which applicants can enroll to prepare for the LSAT, but these Classes are costly. Some applicants incur this cost to take a Preparation Class, but other students do not. Suppose that Law Schools cannot tell whether an applicant took a Preparation
(a) What sort of information could a Law School deduce from an applicant’s LSAT score? What sort of information problem could this correct?
1 University Law Schools typically require applicants to their programs to write a uniform Law School Admissions Test (LSAT).
(c) Now suppose ψ = 1 > so all consumers know that L sells the lowestquality good, and H sells the highest-quality good. If producer L can advertise to make consumers believe he is producing a higher-quality good, discuss his incentive to advertise. Would this increase or decrease price
(b) Now suppose the producers can advertise the quality of their product.If ψ = 0 initially, does increased advertising make the market more or less competitive? Can you relate your answer to the Bertrand paradox?
(a) Suppose producers cannot advertise. Of all the models we have discussed so far, which is most appropriate for this market? Is one model more appropriate for the ψ informed consumers? Would you use a different model for the 1 − ψ uninformed consumers? Why?
4 Consider an industry where two producers sell a product which is differentiated only by quality, in a market where a share 0 < ψ < 1 of consumers are aware of the quality of the product being sold, but the other 1 − ψ consumers are unaware of the quality of each producer’s output. Producer
whether dentist’s services are search goods, experience goods, or credence goods
whether advertising by dentists would be predatory or cooperative
the effectiveness of advertising by dentists
profitability in the dentist industry When making your recommendation, what account would you take of:
quality of dentist’s services
price of dentist’s services
Would you want to allow advertising by dentists, or would you rather ban advertising by dentists? What effect would your recommendation have on:
Suppose you were a government official in charge of regulating advertising by dentists.
3 In many countries, associations of professionals (dentists, for example)argue that advertising should not be allowed in their industry because it increases competition, creating incentives for professionals to cut costs and reduce quality of service.
(d) Use your answers to parts 2b and 2c to verify the optimal share of advertising expenditures out of total revenue according to the monopolist’s rule of thumb: εa/εp = a/(p · q).
(c) Use the demand function to solve for the elasticity of demand with respect to the market price εp and with respect to advertising expenditures εa.
(b) Solve for the two first-order maximization conditions, and use them to solve for the monopolist’s optimal market price p* and level of advertising expenditures a*.
(a) Write out the monopolist’s profit function, as a function of the market price p and advertising expenditures a.
2 A monopolist produces a single output q with constant marginal cost c and zero fixed costs. He faces the following demand function:where p is the market price per unit of output and a is advertising expenditures.
1 In the example in Figure 8.2, what would the payoff matrix look like if advertising by both firms increased each firms revenues by $6 instead of$4? Does this change the Nash equilibrium? Can you relate your answer to the elasticity of demand with respect to advertising and the effectiveness of
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