Purdue ECON 352 – Intermediate Macroeconomics

ECON 352 Intermediate MacroeconomicsPurdue UniversityProblem Set 1Spring 20171. [3 points] Consider an economy that produces and consumes bread and automobiles. Inthe following table are data for two different years.YearYear20102011GoodQuantity Price Quantity PriceAutomobiles100$50,000120$60,000Bread500,000$10400,000$20a. Calculate Nominal GDP in Year 2010 and 2011, and the nominal GDP growthrate.b. Calculate Real GDP in Year 2010 and 2011, with the base year of 2010, and thereal GDP growth rate.c. Suppose a consumer’s basket consists of 100 Automobiles and 500,000 breads.Compute the Consumer Price Index (CPI) in 2011 with 2010 as the base year.Compare it with GDP deflator.2. [3 points] Consider the following Production functions. For each production function, (i)Determine whether each production function has Constant Returns to Scale (CRS),Decreasing Returns to Scale (DRS), or Increasing Returns to Scale (IRS); (ii) FindMarginal Product of Capital (MPK) and state whether it has diminishing marginalproduct; and (iii) Find Marginal Product of Labor (MPL), and state whether it hasdiminishing marginal product.a. F(K, L) = 2K + 2Lb. F(K, L) = K 1/2 L3/2c. F(K, L) = K 1/3 L1/23. [5 points] Suppose the economy has the production function, F(K, L) = K 1/2 L1/2 . Theeconomy begins with 100 units of capital and 100 units of labor. 1 a. Show that this production function is a Constant Returns to Scale productionfunction.b. How much output does the economy produce?c. Suppose output price P=1. What are the wage and rental price of capital?d. If the plague kills half the population (so now there are only 50 units of labor),what is the new level of output?e. What is the new wage and rental price of capital?4. [4 points] Consider an economy described by the following equations:Y = Y = F (K, L) = 1200Y =C + I +GC = 125 + 0.75(Y ? T )I = I (r) = 100 ?10rG = G = 150T = T = 100 a. In this economy, compute private saving, public saving, and national saving.b. Find the equilibrium interest rate.c. Suppose that G rises to 200. Compute private saving, public saving, and nationalsaving.d. Find the new equilibrium interest rate.5. [5 points] Consider a Solow growth model with no population growth. Assume that theaggregate production function has the form Y = K 1/3 L2/3 . People save 20% of theirincome, so their savings rate s = 0.20 and capital depreciates at rate ? = 0.10 . Let per!!worker output be = ! , and per-worker capital be = ! .a. What is per-worker production function? (Express per-worker output as afunction of per-worker capital .)b. What is savings per worker if capital per worker today is 2?c. How much capital depreciates per worker if capital per worker today is 2?d. What is net change in capital? Is the economy at the steady-state when per-workercapital is 2? If not, what is the steady-state level of capital? 2 e. Draw a well-labeled graph of savings per worker and depreciation of capital perworker with per-worker capital on the -axis. On the graph, clearly indicatewhere the steady-state level of capital per worker is. 3