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Intermediate Micro-Economics MICROECONOMICS 3 CLASS #7 GENERAL EQUILIBRIUM – ROBINSON CRUSOE’S ECONOMY Problem #1 Find the ratio of (competitive) equilibrium prices for goods x and y that provide for efficiency of consumption and production, when the production possibilities frontier is: x2 + 4y2 = 200 and the utility function is: U = (xy)0.5. Determine the produced (consumed) amount of goods x and y in this case. Problem #2 Robinson Crusoe decided that he will spend exactly 8 hours per day searching for food. He can spend this time looking for coconuts or fishing. He is able to catch 1 fish or find 2 coconuts in 1 hour. a) Find the formula for Robinson’s production possibilities frontier. b) Robinson’s utility function is U(F,C) = FC, where F is his daily consumption of fish and C – of coconuts. How many fish will Robinson catch and how many coconuts will he find? c) One day a native inhabitant of another island arrived on Robinson’s island. On this other island catching a fish takes 1 hour and finding a coconut – 2 hours. The visitor offered trade at an exchange rate that operates on his island, however Robinson will have to give him 1 fish as a fee for bringing him back to his island. Will Robinson profit from this trade? If yes, will he be buying fish and selling coconuts or vice versa? d) A few days later a native inhabitant of a different island arrived. On his island catching a fish takes 4 hours and finding a coconut – 1 hour. He offered Robinson trade at an exchange rate that operates on his (i.e. the native’s) island but demanded 2 fish from Robinson for bringing him back to his island. If Robinson decides to trade with this island, in production of what will he specialize? e) How will Robinson’s consumption possibilities change in both cases? Which situation will be more profitable for him? (Do not forget about the transportation fee!) Problem #3 On the Veritas island it is illegal to trade with other countries. Only 2 goods are consumed on this island: milk and wheat. There are 40 farms in the northern part of the island. The production possibilities frontier in the north takes the form: m = 60 – 6w, while in the south it is: m = 40 – 2w, where m is the amount of milk and w – the amount of wheat. The economy remains in a competitive equilibrium and 1 unit of wheat is exchanged for 4 units of milk. a) At the given equilibrium prices, in the production of which good will the northern and southern farms specialize? b) Friendly Vikings discovered the possibility to trade with Veritas and offered exchange of wheat for milk at a rate: 1 unit of wheat for 3 units of milk. If the Veritas island permits free trade with the Vikings, a new price ratio will appear on the island. How will production (output) of the farmers in the north and in the south change? c) The Veritas Council of the Elderly is to decide whether to accept the Vikings’ offer. The Council members from the north have 40 votes and the ones from the south – 60. Assuming that each of them votes in accordance with the interest of their part of the island, how will the farmers from the north and south vote? Why are you able to provide a specific answer to the latter question not knowing anything about the consumption preferences of the farmers? Assume that instead of the offered exchange rate of 1 unit of wheat for 3 units of milk the Vikings offered trade at a rate of 1 unit of wheat per 1 unit of milk. How will the output of the farmers from the north and from the south change? How will they now vote? Problem #4 In a certain autarchic economy the production function of good X takes the form X = 100K0.5L0.5, where K is capital, and L is labor. Capital and labor are, however, perfect complements in the production of good Y and employing one unit of capital and one unit of labor allows to produce 100 units of good Y. The total capital resources amount to 100 units. The same is true for total labor resources. a) Present the Edgeworth box and indicate the contract curve therein. b) Derive the production possibilities frontier for this economy and present it graphically. c) If the social utility function takes the form U(X,Y) = XY, what amounts of goods X and Y will be produced? d) If this economy decided to take part in international trade and the ratio of world prices pX/pY exceeded an analogous price ratio in autarchy, how would the production and consumption possibilities change? Which of the goods would be produced in an increased amount and the production of which of them would decrease? Explain the benefits of trade phenomenon. Problem #5 Starbonia is a country where all markets are purely competitive. Services (s) and goods (g) corresponding to point “O” in Figure 1 are produced and consumed in this country. Equilibrium prices of goods and services are identical and equal 1 PLN per unit. Starbonia exercises a protective policy in foreign trade but the government is planning to depart from protectionism. The world prices that will then influence the economy are (per unit): 0.90 PLN for goods and 1.20 PLN for services. a) Assume that the consumption and production levels of goods and services in Starbonia adjust to the new price ratio. Illustrate this in Figure 1. Explain how this adjustment of Starbonia’s economy to the liberalization of trade takes place (i.e. describe the mechanism in a few words – you can refer to the appropriate formulas). Provide your answer to the question, whether Starbonia will profit from departing from protectionism (and in what sense). b) In Starbonia there are 2 factors of production: Young and Old Employees. Point “O” in Figure 2 corresponds to such an allocation of these factors between the production of goods and services, which is a general equilibrium under the protectionist conditions (point “O” from Figure 1). The wages of the Young and Old Employees were identical before the departure from protectionism. The line “Es” shows the changes in factor relations corresponding to the increase in production of services (assuming the equality of wages) and line “Eg” presents this change for the increase in the production of goods. Is it true that trade liberalization causes an increase of the relative wage of the Young Employees? In justifying your answer refer to Figure 2. Figure 1. Production possibilities frontier (transformation curve) Figure 2. Factor allocation Young employees producing services producing Old Es Indifference curve O employees in Starbonia (g) O services ISOg Goods Production possibilities ISO frontier Eg s (transformation curve) goods employees Old Services (s) producing Young employees producing goods .
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