ECON 227 Problems 2, Spring 2011

Economics 227: Intermediate Macroeconomics Assignment 2 This assignment is due before 5PM on Friday, March 18th. 1. In the long-run model, suppose that a stock market crash reduces consumers’ wealth. Use graphs to explain the effect on investment and the interest rate. 2. Suppose that production in an economy is given by the Cobb-Douglas function: Y = F (K, L) = AKαL1−α (a) Suppose the real wage is 1 unit in 2011, 2 units in 2012, and 2.4 units in 2013. If labor earns 1 2 of total income, then what’s average labor productivity? (b) Is it possible for this growth in the real wage to coincide with a constant capital- labor ratio? Why or why not? (c) Now suppose the real wage is some number W P . If a computer virus destroys 15% of Lebanon’s capital stock (and doesn’t change the number of workers), what is the percentage change in W P ? (d) If this computer virus destroys 15% of Lebanon’s capital stock and doesn’t change the number of workers, what is the percentage change in the real interest rate / rental return on capital r = R P ? (e) Now suppose a new virus destroys a further 15% of Lebanon’s capital. Will the magnitude of the change in the real wage be larger, smaller, or the same as it was in part (c)? 3. Suppose production in Lebanon is given by the Cobb-Douglas function Y = AKαL1−α We estimate Lebanon’s GDP is $40 billion, that there are 4 million workers, and total wages are about 64% of GDP. Finally, the interest rate / rental return on capital is r = 10%. Then what’s the estimated value of Lebanon’s capital stock? 4. Consider the CES production function Y = A � αKξ + βLξ� 1 ξ (a) Show that the CES production function is CRS. (b) If production is CES, what are the real wage and rental return on capital? (c) Show that Euler’s Theorem holds. 1