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# Econ 427 Professor Ickes Energy Economics and Energy Security Spring 2013 Homework Assignment #1: Due: Thursday, January 24, at the start of class.

Econ 427 Energy Economics and Energy Security Professor Ickes Spring 2013 Homework Assignment #1: Due: Thursday, January 24, at the start of class. 1. What does the cross-country relationship between income per-capita and energy use per-capita look like? (a) If we plot US energy consumption since 1950 is there any trend? If so, what does it look like? (b )I fwep lo tUSene rgycon sump t ionpe run i to frea lGDPs ince1950wha tdoe si tlook like? (c) Do we use more or less coal today that we did in 1900? 2. Suppose that the aggregate production function is given by = 1 ,where and are capital and energy, respectively, and  1. Show that the elasticity of substitution of this production function is unity. [Hint: note that the marginal product of capital is  1 1 , and the marginal product of energy is (1 ) ] 3. Suppose that the aggregate production function is given by =[(1 ) 1 +  1 ] 1 where and are as before. Suppose that there are competitive markets so that = =  1 1 Let be capital’s share, and (1 ) be the energy share, and let (a)Showthatas rises, energy’s share of output falls only if  1 (b) If = what happens to output as becomes more and more scarce? (c) If = 0 what happens to output as becomes scarce? (d)Whathappensi f =1? 1

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