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(ECON514)901bdf - EC51409Midterm1AK.pdf
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Mid-Term Exam # 1
Economics 514
Macroeconomic Analysis
Tuesday, October 13th , 2009

Write your answers on this white exam. Do not write your answers on the blue book! Do not hand in your blue book!

1.
Labor Supply Workers preferences are given by a log/log utility function.





where Ct is consumption and lst is leisure. Assume that workers have 1 day available for work, leisure, and sleep, Sleep + Lt + lst = 1. Assume that non-labor income is equal to, so the workers budget constraint is



a.
Solve for optimal labor, leisure, and consumption when Sleep = (8 hours) and real wages is w = 1. Assume that the worker oversleeps and Sleep = . (12 hours). What would be labor, leisure, and consumption?




The first order condition is that the marginal cost of leisure is equal to marginal benefit. The marginal cost is the marginal untility of consumption multiplied by the real wage. The marginal benefit is the marginal utility of leisure









ls
L
C

Sleep = 8








Sleep = 12











b.
Draw a picture of the optimal consumption and leisure choice when Sleep = and when Sleep = . . Use budget constraints and indfference curves to demonstrate the different potential outcomes.





ls

C

1-Sleep

1-Sleep

2.
Forecasts of economic growth. Brazil and Columbia have the same level of labor productivity, y0 = 36, and capital productivity, = 1. ), a population growth rate of 2% (n = .02), and a depreciation rate of 6% ( = .06). Brazil has an investment rate of 20% (sBZ = .2). Argentina has an investment rate of 10% (sCL = .1). Use the following table to answer your questions:




x
1.01
1.02
1.03
1.04
1.05
1.06

x^20
1.22
1.49
1.81
2.19
2.65
3.21

x
1.07
1.08
1.09
1.1
1.11
1.12

x^20
3.87
4.66
5.60
6.73
8.06
9.65



a.
Brazil and Columbia have Cobb-Douglas production functions of the form.





where both share the same technology level, At. Assume a technology growth of 2% (i.e. gA = .02). Solve for the level of technology at time 0, A0. Assume that 20 years from now, both countries are on their balanced growth path. Calculate the level of labor productivity in both countries. What is the ratio of labor productivity in country A relative to country B?

logy level is


Steady state capital productivity is



For Brazil, this is . so labor productivity at the balanced growth path is
For country B, steady state capital productivity is 1, so on the balanced growth path, the level of productivity is 53.64. The ratio is the square root of 2.



75.86



53.64








b.
Assume Country A and B both have an AK production function:





where both share the same constant technology level, A. Calc