Microeconomics

Steel manufacturing in the US requires only one input: labor. Steel is produced by a representative rm under perfect competition according to the production function 1 L = L St ) 2 Throughout this problem assume that the wage in the United States is 1. {1} {4 minuta) Suppose that United States can freely import and expert steel. Foreign supply of steel is supplied with perfect elasticity at a price of 1. How much steel is produced in the US\"? Car manufacturers use steel and labor to make cars. Both steel and labor are variable inputs and cars are produced by a. representative firm under perfect competition according to the production function F[L,S) = \"3+ vi?) {2) {1D minutes} Now suppose the price of steel is p3. Solve for the supply function of US car manufacturers [quantity supplied as a function of the price of cars, is... and the price of steel a)- {3} {3 minutes} Assume the US freely trades steel, where the world price of steel is 1 as before. 1What is the supply curve for cars? {4] {3 minutes] Suppose that the supply of cars from foreign producers is perfectly elastic at p = lll {the world price of cars is Hill}7 and the US demand for cars is Q = lS lP. {a} {4 minutes] Supposing that there is free trade in the car market as well as the steel market, calculate the equilibrium price and quantity of cars consumed {purchased} in the United States. Does the US imp-ort- orerport cars andhow many ow the US import or export? (b) (4 minutes) Calculate consumer and producer surplus under trade. (5) (15 minutes) The US government is unhappy with steel imports and decides to impose a 200 percent tariff on imported steel so that the price of imported steel is now 3 when importing from abroad. (Continue to assume that the US domestic steel market operates in perfect competition with production function S(L) = ;1) (a) (2 minutes) What is the price of domestic steel? Will car manufacturers choose to use domestic or foreign steel? (b) (5 minutes) Calculate the new equilibrium in the US market for cars, continuing to assume that cars are traded freely at a world price of 100. Does the US still export cars?\fAn economy has two agents, Bill and Bob. Bill has $110, and Bob has $200. Utility of agents in this economy is characterized by the following function of income: U = u(y) = [ log(y - 60) if y 160 The minimum level of income possible in this economy is 60. Each agent is about to choose a new business venture, and has a choice between project A and project B. Neither project requires any investment up front. Project A yields revenues of 20 with probability = and revenues of -10 with probability -. Project B yields revenues of 4 with probability one-half and revenues of 5 with probability one-half. Throughout this problem, assume that fractional income is possible. (a) (5 points) Which project would each agent choose? Provide intuition for your answer. (b) (5 points ) If Bill and Bob each choose an investment project each year and receive the associated income for 20 years, will the expected gap in their incomes be larger or smaller at the end of this period than it was initially ? How does this relate to attitudes toward risk? You do not need to calculate income over 20 years, just provide intuition. (c) (10 points) Now, assume that there is a job available that provides fixed wage income. What salary would the job have to provide in order to induce Bill to take the job rather than entering a new business venture? What salary would the job have to provide in order to induce Bob to take the job? Which is higher, and why? Algebraic expressions are acceptable as answers