(1) Suppose the demand for a certain good is given by the equation: P = 40 - 2Q and the supply for the same good is given by equation: P = 10 + Q. Calculate the Producer Surplus at the market equilibrium. (II) The following table shows how many hours it would take to produce one meter of cloth or one kilogram of wheat for country A and country B. Cloth wheat Country A 1 hour per meter 3 hours per kg Country B 2 hours per meter 4 hours per kg Assume that Country A has 60 million hours of labor. Country A is wondering about two possible combinations of production: 20 million meters of cloth and 10 million kg of wheat OR no cloth but 20 million kg of wheat. Which combination achieves production efficiency?
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2. Suppose that the ROW has the same technology (10 labor and 5 capital to produce a ton of steel, 2 labor and 4 capital to produce a ton of wheat) and the same amount of labor (240) but 360 capital. a. The ROW capital constraint is Q + Qw = 360 or Q = -1.25Q. b. Graph the labor constraint, the home capital constraint, and the ROW capital constraint. c. The ROW production bundle of steel and wheat that fully employs both factors is Bo tons of steel and g0 tons of wheat. Compare the relative production of steel to wheat across countries. The relative supply of steel to wheat for the ROW is higher than for home. d. Compare the relative abundance of labor to capital across countries. Which country is relatively abundant in labor to capital? Compare the relative intensity of factor use across goods. Which good makes relatively intensive use of labor to capital? What does each country import and export? Home imports wheat and Home exports steel. ROW imports wheat and ROW exports neither.
Supreeta N.
Assume wheat in the U.S. is grown in a perfectly competitive market. Let the market supply of wheat be Qs = 5P - 150 and the market demand for wheat be Qd = 200 - 2P, where Q represents the amount of wheat per year in billions of bushels and P is the price of wheat per bushel. Suppose that wheat farming creates agricultural runoff (pollution) with an external cost of EC = 0.05Q^2. (a) Calculate the socially optimal quantity of wheat that should be produced each year. (b) Calculate the competitive market equilibrium price and quantity. Calculate the size of any deadweight loss associated with the competitive market equilibrium. (c) Suppose that wheat farms combine into a single monopoly producer whose total (private) costs are given by C = 30Q + Q^2 + 10. Calculate the profit-maximizing quantity of wheat produced and the price. Would the monopoly firm produce the socially optimal quantity of wheat that you found in part (a)? As a social planner, would you prefer a monopoly market or a competitive market? Explain by calculating the size of the deadweight loss associated with the monopoly outcome and comparing it to the size of the deadweight loss associated with the competitive market outcome. (NOTE: The deadweight loss should be calculated relative to the social optimum, not the competitive market outcome.)
Akash M.
Consider a world with two countries and three goods. Both countries can use linear labor-only technologies to produce these goods. The labor productivities in the home country are denoted by zn,H, and in the foreign country by zn,F, where n ∈ {1, 2, 3}. These productivities are positive and satisfy z1,H / z1,F < z2,H / z2,F < z3,H / z3,F The home- and foreign-country labor supplies LH and LF are supplied inelastically, and consumers have identical preferences over the three consumption goods, described by the utility function u(c1, c2, c3) = ̢1 ln(c1) + ̢2 ln(c2) + ̢3 ln(c3), where ̢1 + ̢2 + ̢3 = 1. Write Cn,j for consumption of good n in country j, pn for the world price of good n, and wj for the wage in country j, where n ∈ {1, 2, 3} and j ∈ {H, F}. Assume that the equilibrium pattern of specialization is such that both countries produce strictly positive amounts of good 2. a. Determine the wage ratio wH/wF and the relative prices pn/wj for n ∈ {1, 2, 3} and j ∈ {H, F}. b. Given these wages and prices, determine Cn,j for n ∈ {1, 2, 3} and j ∈ {H, F}. c. Combine the results from a and b with market clearing conditions to determine the amounts of labor ln,j used to produce good n in country j, for n ∈ {1, 2, 3} and j ∈ {H, F}.
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