Practice Solow II

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University of Illinois at Urbana-Champaign 
Department of Economics 
Econ 490 – Topics in Economic Growth 
Instructor: Paulo Vaz 
Spring 2014 
 
 
Practice Questions – Midterm II 
 
 
1) Development Accounting - Consider the following data on the fictional countries of 
Sylvania and Freedonia. The production function is y=Akαh1-α, in per worker terms, 
where α = 0.5. 
 
 Sylvania Freedonia 
Output per worker, y 100 200 
Physical Capital Per Worker, k 100 100 
Human Capital per Worker, h 25 64 
 
 
a) Calculate the level of productivity, A, in each country 
b) Calculate the countries’ relative levels of output if all differences in output were 
the result of productivity. 
c) Calculate the countries’ relative levels of output if all differences in output were 
the result of factor accumulation 
 
 
2) Growth Accounting - The following table provides data on the annual growth rates of 
output, physical capital, and human capital per worker for three countries. For each 
country, calculate the growth rate of productivity and factor accumulation. In which 
country does factor accumulation account for the largest share of growth? In which 
country does productivity account for the largest share of growth? 
 
Country Growth rate of 
output per worker 
(%) 
Growth rate of 
Physical Capital 
Per Worker (%) 
Growth rate of 
Human Capital Per 
Worker (%) 
Argentina 0.66 0.31 0.52 
Uruguay 1.82 1.83 0.51 
Panama 1.73 0.90 0.84 
 
 
3) Consider a country described by the one-country model. Suppose that the country 
temporarily raises its levels of γA. Draw graphs showing how the time paths of output 
per worker (y) and productivity (A) will compare under this scenario with what would 
have happened if there had been no change in γA. 
 
4) Consider the one-country model of technology and growth that was presented in 
in class. Suppose that L=1, µ=5, and γA= 0.5. Calculate the growth rate of output per 
worker. Now suppose that γA is raised to 0.75. How many years will it take before output 
per worker returns to the level it would have reached if γA had remained constant? 
 
5) Consider the two-country growth model. Suppose that γA,1> γA,2 and that the two 
countries are in the steady state. Suppose now that country 1 raises the fraction of the 
labor force that is doing R&D. Draw a picture showing how the rates of growth in 
countries 1 and 2 will behave over time. 
 
6) Consider the two-country model. Suppose that γA,1 > γA,2 and that the two countries are 
in the steady state. Now suppose that Country 2 raises the fraction of labor force that is 
doing R&D so much that γA,1 < γA,2. Draw the picture showing how the rates of growth in 
Countries 1 and 2 will behave over time. 
 
7) Consider the two-country model of Section 8.3. Suppose that the cost-of-copying 
function is: 
µc=µi(A1/A2)-β 
 
where 0<β<1. Assume that the two countries have labor forces of equal size. 
 
a) Using this function, solver for the steady-state ratio of technology in the leading 
country to technology in the follower country (i.e. , A1/A2) as a function of the 
values of γA in the two countries. Show how this depends on the values of β and 
explain what is going on. 
b) Assume that β=1/2, µi=10, γA,1=0.2 ,γA,2=0.1. Calculate the steady-state ratio of 
technology in Country 1 to technology in Country 2. 
 
9) In the two-sector (Urban and Rural) model of an economy, use a diagram to show how 
a minimum wage in the urban sectors would lead to an inefficient allocation of labor. 
 
 
10) Consider a country in which there are two sectors, called Sector 1 and Sector 2. The 
production functions in the two sectors are: 
 
Y1 = (L1)1/2 
Y2 = (L2)1/2 
 
where L1 is the number of workers employed in Sector 1 and L2 is the number of 
workers employed in Sector 2. The total number of workers in the economy is L. The 
only difference between the sectors is that in Sector 1 workers are paid their marginal 
products, whereas in Sector 2 they are paid their average products. Workers move freely 
between sectors so that the wages are equal. Calculate how many workers will work in 
each sector.