Answer the given questions

This question studies the co-existence of different currencies,

Time is discrete with an infinite horizon. Each period consists of two subperiods. In the day, trade is bilateral and anonymous as in Kiyotaki and Wright (1989) (call this the KW market). At night trade takes place in a Walrasian or centralized market (call this the CM). There are two types of agents, buyers and sellers, and the measure of both is normalized to 1. The per period utility for buyers is u(g) + U(X)-H, and for sellers it is -q+U(X)-H, where q is the of the day good produced by the seller and consumed by the buyer, X is consumption of the night good (the numeraire), and H is hours worked in the CM. In the CM, all agents have access to a technology that turns one unit of work into a unit of good. The functions u, U satisfy the usual assumptions; I will only spell out the most crucial ones: There exists X (0,00) such that U'(X) = 1, and we s define the first-best quantity traded in the KW market as q = (g: u'(q)-1}. We will assume that there are two types of money, my and my. There are also two types of sellers. For reasons that we will leave out of the model, Type-1 sellers, with measure a (0, 1), do not recognize my, thus, they accept only the local currency my. Type-2 sellers, with measure 1-a, recognize and, hence, accept m, as well as m. Hence, local currency has a liquidity advantage over the foreign one, since it is recognized by all sellers. All buyers meet a seller in the KW market, so that o is the probability with which a buyer meets a type-1 seller, and 1-0 is the probability with which she meets a type-2 seller. In any type of meeting, buyers have all the bargaining power. The rest is standard. Goods are non storable. The supply of each money is con trolled by an individual authority, and evolves according to M. (1+) M., New money (of both types) is introduced, or withdrawn if ,

Part C 1. Consider an economy where consumers buy land (X) and computers (Y) and are characterized by the utility function U= YdXH, Suppose the computer production Bequires a homogenous input 2., and a service composite v which is created from differentiated services s. They are combined according to the production mction for computers: Y = y'all", where v = ( E- s")\"". Labor is used in producing differentiated services s, acccrmng to Li = a + bsi, while a single unit of labor is required for each unit of Z produced, or Z = LI. a) Assume further that z is uadable across borders, while services are not. Explain and show how agglomeration economies arise in this context. b) Suppose the country has 10 regions, one of which is the center where computers are produced, Each region has an equal endowment of land, while the nation's labor force is free to migrate to any region within the country. Will migration result in the equalization of nominal wages across regions? Show and explain why or why not. c) Now suppose that a pioneer rm from the center decides to extend production to another region. While there is a xed cost for pioneering activities, pioneering activities reduce the transportation costs associated with the shipment of the homogenous input 2: across regions. Provide examples of pioneering investments that are specic to the pioneering rm versus those that will provide spillovers to other rms. cl) How could you empirically test whether pioneering activities appear to affect the geographic distribution of economic activity? Propose an empirical specication, and explain what you would expect to nd if pioneering activities matter. Part C {continued} 2. Consider the North American Auto market as represented by a U.S. and German rm, both of which are located in North America and producing for North American customers. When the NAFTA was implemented, it specied that rms purchase least ypercent of their inputs from NAFTA partners [USa'MexioofCanada} to qualify for preferential NAFI' A benets. a) Consider the case of the German rm and its assembly of cars in Mexico. The rm's production process requires it to combine an engine with a specied set of parts. Show how the shadow price for Mexican and German-origin auto parts depends on the content requirement 7. What is the intuition for your result? h} Now assume that the production functions for the US. and German rm are given by X\" = 21,\" an'\" and X3 = zbzm'", where 2., represents inputs that are rm the NAFTA block, and Zn, represents inputs that originate outside the block, and Wm). Inputs prices are qt. and tine respectively. The inverse demand for autos is p = a-bX, where X = X\2. (i) Explain the eonoept of opportunin loss. and show that the minimum opportunity loss is equal to the Expected Value of Perfeet Information. (ii) The failure rate in a partieular examination is estimated to be 40%. Construct a table showing the probabilities of II}. 1. 2 . . . 5 students failing in a sample of five. (iii) 151} graduate entrants are due to talte their rst professional aooounting exam at the Institute of Certiable Aeeountants. The probability distribution for the failure rate is estimated in the following table: Fuiiure rate Probabiiity 0.1 Ill {LE 0.2 0.3 0.3 (1.4 [13 11.5 '11 Each failing student is entitled to a t] refund on professional fees. The Institute's senior tutor is eondent that she eould ensure a failure rate of {1.1 by holding an intensive revision course, at an east to the Institute of 31m. Advise the Institute on whether the revision eeurse should take place. A tutorial test of ve students resulted in no failures. Use this information to revise the failure rate probability distribution, and hence reassess the revision course. 3. 'Despite being a small local shopkeeper I can always beat the priee that Woolworths charge for the same product. Woolworths must pa}r rent on its store while I own my shop and have no rent to pay.' Disease. 4. A firm keeps a record of sales and prices over the past seven months, resulting in the following table: Price (f/ton) Sales (tons) Nov. 1985 7.5 84.5 Dec. 8.0 82.0 Jan. 1986 8.0 84.0 Feb. 7.2 92.0 March 7.0 95.0 April 8.0 92.0 May 8.5 91.5 Use these observations to estimate demand as a linear function of both price and time. Utilise this function to estimate demand for the following month, on the assumption that: (a) price remains unchanged, (b) price increases to f9/ton