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(ECON343)Midterm-Spring2009.pdf
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Midterm Exam
. There are 3 questions; you have to answer all of them. -Problem 1: 30 points -Problem 2: 30 points -Problem 3: 40 points
. You have 2 hours and 30 minutes to complete this exam.
GOOD LUCK !

1. [30 points]
(a) [3 points: 1 + 1 + 1]
Suppose the per capita GDP of an economy is growing at the rate g. If yt denotes per capita GDP in any period t and y0 denotes the per capita GDP in period 0, then find out the expressions of the following in terms of g and y0:
(i)
per capita GDP in period 1 (that is, y1),

(ii)
per capita GDP in period 2 (that is, y2),


(iii) per capita GDP in any period t (that is, yt).
(b) [14 points: 6 + 4 + 4]
[Hint: To make your calculations simpler, always use the approximation lne (1 + x) x for small values of x.]
(i)
Consult Table 1 and use the expression derived in part a (iii) to calculate the growth rates of per capita GDP of United States and China over the 19-years period 1973- 1992.

(ii)
Suppose both China and the United States maintain the same growth rates you have just calculated. Then, starting from 1992, how long will it take China to catch up with the level of the per capita GDP of the United States?


(iii) The Chinese people do not want to wait that long; they want to catch up with the US per capita GDP level in just next 25 years (starting from 1992). How fast the Chinese per capita GDP has to grow in order to achieve this target?
(c) [13 points: 2 + (7+ 2 + 2)]
The Solow growth model predicts that there is a steady-state level of per capita income to which the economy must converge, irrespective of its historical starting point. This is the convergence hypothesis.
(i)
What kind of relationship between growth rates of per capita income and the initial value of per capita income does the convergence hypothesis predict?

(ii)
Take a very careful look at Table 2 and Table 3 (that are prepared from Table 1) along with Table 1.


-Does the evidence in Table 2 support the prediction of the convergence hypothesis? Explain carefully.
-Does the evidence in Table 3 support the prediction of the convergence hypothesis?
-In light of the empirical research on convergence hypothesis, what information (data) is missing in these tables that was found to be essential to evaluate properly the prediction of the convergence hypothesis?
2. [30 points]
Let us recall the Dalton Principle. For this we define the concept of a regressive transfer: a transfer of income from the not richer individual to the not poorer individual. (Progressive transfer can be defined symmetrically: a transfer from the not poorer individual to the not richer individual) The Dalton principle states that if one income distribution can be achieved from another by constructing a series of regressive transfers, then the former distribution must be more unequal than the latter.
(a) [5 points]
Consider the following two income distributions:

Distr