What is China's budget constraint? Describe the maximisation problem of China, set up the Lagrangian, and derive China's optimal consumption of smartphones and rice as a function of the price of smartphones ps, the price of rice p, and the wage w.
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- A farmer produces both green beans and corn. The farmer must give up 31 bushels of corn to get 7 more bushels of green beans. If the rate of transformation (or tradeoff) between the two goods is constant, then the opportunity cost of 1 bushel of green beans in terms of bushel of corn is? The result should be given to two decimal places in absolute value (e.g if the result is 3.678, write 3.68, if the result is -3, write 3.00.) Your Answer:Suppose two economies Home (H) and Foreign (F) produce two goods, bread and wine, with only one production factor: labour. Production technology, expressed as marginal product of labour (MPL), is given in the following table: Technologies expressed as MPL Bread Wine Home 1/6 1/12 Foreign 1/4 1/2 Suppose that Home has 2400 units of labour and Foreign has 1800 units of labour. a. ) Derive the Production Possibilities Frontier (PPF) and the Consumption Possibility Frontier (CPF) for Home and Foreign, with bread on the horizontal axis and wine on the vertical axis. What is the autarky equilibrium price of bred relative to wine in each country? b.) What country has the absolute advantage in producing each good? What country has the comparative advantage in producing each good? Briefly explain the difference between these two concepts. Suppose both countries are now free to trade. The world relative price of bread is 1. c. What is the pattern of specialisation and trade?…Suppose there are two countries, Home and Foreign, that produce two goods, fish (F) and edamame (E), using only labor. In the Home country 6 units of labor are required to produce each unit of fish and the same for each unit of edamame. In the Foreign country, 2 units of labor is required to produce each fish and 3 units of labor are required for each unit of edamame. Each country has a labor force of 30 units available for production. Suppose further that consumers in both countries have identical Leontief preferences, utility function U(CF, CE) = min(CF, CE), meaning that they want to consume the two goods in a fixed proportion of one-to-one, i.e. CF = CE (there is no substitution between the goods). Suppose now that the labor force of the Home country is 6 times as big (i.e. 180 units, instead of 30). How does this increase in labor force at Home change the pattern of trade? Will the gains from trade for the Home country be higher or lower now? What happens to the welfare of the…
- Consider a specific-factors model where two Countries, Denmark and Tanzania, use labor to produce cake (C) and helicopters (H). However, arable land (A) are a factor specific to cake, and jerrycans (J) are a factor specific to helicopters. Suppose that Tanzania has L = 100 workers, J = 40 jerrycans, and A = 1000 arable land. The production functions and marginal products of labor for cake and helicopters are: C = 4 x Lc %D 0.5 x A0.5 MPLC = 2 x Lc0.5 x A0.5 H = 4 x LH0.5 x J0.5 MPLH = 2 x LH-0.5 x J0.5 In Tanzania, the price of crystals is 20 and the price of hyperdrives is 200. In this case, the wage rate will be ___ and the cake industry and will be employed in the helicopter industry. %3D workers will be employed in workersConsider a specific-factors model where two Countries, Denmark and Tanzania, use labor to produce cake (C) and helicopters (H). However, arable land (A) are a factor specific to cake, and jerrycans (J) are a factor specific to helicopters. Suppose that Tanzania has L = 100 workers, J = 40 jerrycans, and A = 1000 arable land. The production functions and marginal products of labor for cake and helicopters are: C = 4 x Lc0.5 x A0.5 MPLc = 2 x Lc-0.5 x A0.5 H = 4 x LH0.5 x J0.5 MPLH = 2 x LH-0.5 x J0.5 In Tanzania, the price of crystals is 20 and the price of hyperdrives is 200. In this case, the wage rate will be ________ and ________ workers will be employed in the cake industry and __________ workers will be employed in the helicopter industry.Consider Robinson Crusoe who lives alone on the island. He can produce two goods eggs (good X) and yoghurt (good Y). The only input to the production of these goods is his labour. He works 12 hours per day and sleeps for 12 hours - there is no time to play- this is a very grim economy... Let Lx denote the amount of time devoted to producing eggs (good X) and Ly denote the amount of time devoted to producing yoghurt (good Y). Eggs are produced using the production technology X = 5√Lx and yoghurt is produced using the production technology Y = 4Ly. His preferences for eggs and yoghurt are described by the indifference curves with marginal rate of substitution MRSxy = Y/X. a) What is the production possibility frontier (PPF) for this economy? Hint: find how much labour is required to produce x eggs and y yoghurts and then use the resource constraint that the total labour available is 12 hours. What is the slope of the PPF? Remember, it is called MRT.
- Consider a specific-factors model where two countries, Denmark and Tanzania, use labor to produce cameras (C) and helicopters (H). However, apertures (A) are a factor specific to cameras, and jerrycans (J) are a factor specific to helicopters. Suppose that labor is freely mobile between both industries. Suppose that by opening up to trade the price of cameras in Tanzania falls by 5%, wages fall by 3%, and the price of helicopters does not change. Use the following information to determine how these affect the rental rates of apertures and jerrycans: Cameras: Sales Revenue 30 Cameras: Labor Payments 20 Cameras: Apertures Payments 10 Helicopters: Sales Revenue 30 Helicopters: Labor Payments 10 Helicopters: Jerrycans Payments 20 In this case, the rental rate to apertures would change by _______ % and the rental rate to jerrycans would change by ______ %. As a result of these changes: A. Owners of apertures are made worse off, and owners of jerrycans are made better off…Consider an economy inhabited by George and Harriet, whose utility functions are Ug : (ac)² (bc)2 Он тан + 2bн The total quantities of ale and bread that can be produced by the economy are a and b, and they are constrained by the production function b = 2(10 – a)/2 There are infinitely many Pareto optimal allocations. In one of them, Harriet's utility is 8. a) An allocation in this economy is described by a list of four variables. What are these variables? b) What four equations describe the Pareto optimal allocation in which Harriet's utility is 8? c) Find this Pareto optimal allocation.Consider a trade economy with two people (A and B) and two goods (1 and 2). Person A's utility function is U A = x1x2 where xi is A's consumption of good i E (1, 2). Person B's utility function is U B = y1 + y2, where yi is B's consumption of good i = (1, 2). There are 20 units of each good in the economy. Which of the following allocations are efficient? (a) x1 = 10, x2 = 10, y1 = 10, y2 = 10. (b) x1 = 7, x2 = 7, y1 = 13, y2 = 13. (c) x1 = 0, x2 = 0, y1 = 20, y2 = 20. (d) x1 = 15, x2 = 10, y1 = 5, y2 = 10. (e) x1 = 12, x2 = 12, y1 = 6, y2 = 6.
- What is the axiom of consumer choice that implies that consumers spend all their income in order to maximize utility? and Explain the main assumption behind a concave production possibilities frontierThe U.S. imports lumber among other goods from Canada. The lumber has been the topic of political dialogue between the 2 countries in the past few days. So let’s take X as ‘lumber’ and Y as ‘other goods’. Suppose the Canadian lumber and other exportable goods are produced with the following production Possibilities frontier (PPF): X2 + Y2 = 900 Suppose the U.S. utility function for the Canadian lumber, X, and other exportable goods, Y, is: U = X Y a. Derive the conditions necessary to determine the ‘Optimal Product Mix’ discussed in chapter 10. b. Draw the PPF (partial just the first quadrant) with Y on the vertical axis. On the same graph, draw at least one indifference curve so as to show the “optimal product mix’. Can this graph represent the ‘pure exchange’ economy? Explain why or why not. c. Now draw in a price line that can make the ‘optimal product mix’ a competitive exchange equilibrium. Can…i Consider the information in the table below. Himma and Därude are two countries that can produce two goods, vinegar (measured in liters) and sugar (measured in kg). The only factor of production is labor. The assumptions of the Ricardo model are satisfied. Unit consumption coefficients: Vinegar Himm 1/6 Därude 1/4 lb 1c Sugar 1/4 1/2 Which country has a comparative advantage in the production of sugar? Why? Which country will produce which good given that the relative price of sugar in trade is established at 1.75 (PS). trade is established at 1.75 = 1,75)? PS = PA 1d PS (P₁ = 1)? PA How does your answer change if the relative price of sugar at trade is instead 1