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midterm1-solution

# midterm1-solution - UNIVERSITY OF VIRGINIA ECON 3020 003...

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UNIVERSITY OF VIRGINIA ECON 3020 - 003: INTERMEDIATE MACROECONOMICS MIDTERM 1 - Solution key 1. (a) From the Solow growth model we know that in the steady state capital is given by: K = sA d 1 1 ¡ fi L Therefore K TL K OL = s TL A TL s OL A OL 1 1 ¡ fi = 0 : 15 £ 4 0 : 3 £ 1 3 = 2 = 2 : 828 Now Y TL Y OL = A TL K 1 = 3 TL A OL K 1 = 3 OL = A TL A OL K TL K OL fi = 5 : 656 The ratio of consumption is given by: C TL C OL = (1 ¡ s TL ) Y TL (1 ¡ s OL ) Y OL = 6 : 869 (b) Capital for OL will increase by ¢. This will increase output. It will also increase investment by sY 0 ¡ sY and depreciation by dK 0 ¡ dK = d ¢. However because of diminishing returns the increase in investment will be smaller than the increase in deprecation. Therefore over time capital will fall back to its steady state. So over the long run Obsolitia’s economy will move to its original state. The graph is a standard Solow graph. 2. (35 points) (a) In this model K is flxed. Wages will be given by: w = 2 3 A K L 1 = 3 Let L 0 = 2 = 3 L be the population after the plague. Similarly, let w 0

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midterm1-solution - UNIVERSITY OF VIRGINIA ECON 3020 003...

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