NAME_____________________________________________
Econ 120: Economic Development, UCSC, Spring/06, Instructor: Jonathon Adams-Kane
MIDTERM EXAM – MAY 8 th
2006
Please read the instructions for each section carefully
SECTION A: (40 points) You must answer four, and only four, of the five questions
(numbered in bold type) in this section.
A.1
(10 pts.) Show in a diagram an S-curve and a 45-degree line, carefully labeling the axes. Are all three points of intersection stable equilibrium points? Explain.
See textbook, pages 148-153.
A.2
(10 pts.) Explain the basic idea behind the Big Push model. A diagram is not required.
See textbook, pages 155 10 159.
Sample answer: Each modern firm's investment decision has a beneficial externality to other modern firms, in that its workers' wage premiums create demand for other firms' products. For some range of the wage premium, multiple equilibria may exist. In one equilibrium, few modern firms invest, and given the actions of the other firms, it is in an individual firm's best interest not to invest because market demand is low. In another equilibrium, many modern firms invest, this creates market demand (through the wage premium), and it is in the best interest of an individual firm to invest.

A.3
(A.3.a) (4 pts.) What are the four indicators that make up the Human
Development Index?
Avg. income (PPP), life expectancy, adult literacy, gross school enrollment rate.
(A.3.b) (6 pts.) What is the exact formula for the Human Development Index?
HDI

1
3 

 ln( ln income )
40 , 000

 ln ln
100
100 



1
3

 l .
e .
85


25
25



1
3 


2
3


 literacy
100


0
0




1
3


 enrollment
100

0

0






A.4
(A.4.a) (4 pts.) Write a production function typically assumed in Kremer's Oring theory. e.g. F(q
1
,q
2
,q
3
)= q
1 q
2 q
3
, or BF(q
1
,q
2
,q
3
)= q
1 q
2 q
3
(A.4.b) (6 pts.) Explain the basic idea behind Kremer's O-ring theory. A diagram is not required.
See textbook, pages 166-171
A.5
(A.5.a) (7 pts.) Without writing any math, explain the basic difference between the exchange rate method and the purchasing power parity method of measuring national income, and explain the motivation for using the purchasing power parity method.
For each country, the exchange rate method multiplies the quantity of each good produced by the price of that good in that country, sums this product across goods, and converts that sum into a common currency using a market exchange rate. The PPP method multiplies the quantity of each good produced by its price in a chosen country, and uses those same prices across all countries.
The PPP method is useful to compare the physical quantities of goods produced across countries since the same weights (prices) are used to aggregate quantities across countries. Also, it is useful for comparing the purchasing power of countries' incomes, since it adjusts for price differences across countries.

(A.5.b) (3 pts.) Briefly, why do purchasing power parity measures of income tend to show a smaller difference between low-income and high-income countries than other measures of income?
Low-income countries tend to have lower prices, when prices are expressed in a common currency using market exchange rates.
SECTION B: (40 points) You must answer two, and only two, of the three questions
(numbered in bold type) in this section.
The following income distribution data are for Brazil.
Quintile
Lowest 20%
Second quintile
Third quintile
Fourth quintile
Highest 20%
Percent Share
2.4%
5.7%
10.7%
18.6%
62.6%
Brazil's total national income: $1 billion per day
Brazil's population: 150 million people
B.1
(B.1.a) (8 pts.) Graph the Lorenz curve from the Brazilian data given above, carefully labeling the axes. On the axes, label all values that correspond to the five points that make up the Lorenz curve.
See textbook, page 198. y-axis values: 2.4, 8.1, 18.8, 37.4, 100 x-axis values: 20, 40, 60, 80, 100
(B.1.b) (3 pts.) Show how to find the Gini coefficient, graphically (do not actually calculate it numerically).
See textbook, page 200.

(B.1.c) (6 pts.) Suppose that each household makes the average income for its quintile (that is, assume that there is no inequality within quintiles).
Using a poverty line of $1 per day per capita, what is the headcount
(i.e. the measured number of poor people)? What is the average income shortfall (AIS)?
2.4%($1 bil.)/20%(150 mil.) = $0.80 per day per person (1st quintile poor)
5.7%($1 bil.)/20%(150 mil.) = $1.90 per day per person (2nd not poor)
H = 20%(150 mil.) = 30 million, AIS = $1 - $0.80 = $0.20
(B.1.d) (3 pts.) Suppose one percent of total national income were transferred from the highest-income quintile of households to the lowest-income quintile of households. Assume no other changes in the economy.
What is the quantitative effect on the headcount?
1st quintile's daily income per capita increases by 1%($1 bil.)/30 mil.
= $0.33, to $1.13. They are no longer poor, so H falls to 0.
B.2
(B.2.a) (3 pts.) Using the Brazilian data given above, what is the growth rate of total national income if the highest-income quintile's income increases by 10%, and all other quintiles' incomes remain constant?
G = 62.6%(10%) = 6.26%
(B.2.b) (3 pts.) Using the Brazilian data given above, what is the growth rate of total national income if the lowest-income quintile's income increases by 10%, and all other quintiles' incomes remain constant?
G = 2.4%(10%) = 0.24%
(B.2.c) (4 pts.) Referring to your answers to parts (a) and (b), briefly explain why the growth rate of national income is not a very useful measure of social welfare, even relative to other measures of social welfare that are just aggregations of quintiles' income changes.
The answers to parts (a) and (b) show that a given percent change in a quintile's income comprises a larger share of national income when that quintile's level of income comprises a larger share of national income, unsurprisingly. But from the standpoint of social welfare, there is no clear reason why a 10% increase in high-income households' income is so much more beneficial to society than a 10% increase in low-income households' income, so the growth rate of national income is not a very good social welfare measure.

(B.2.d) (6 pts.) Write an example of an Ahluwalia-Chenery welfare index
(ACWI) that reflects some policy objective of your choosing, and briefly explain how the numbers you chose reflect that policy objective.
Sample answer: ACWI = 0.5g
1
+ 0.2g
2
+ 0.1g
3
+ 0.1g
4
+ 0.1g
5
The weights in this ACWI reflect the social goal of alleviating poverty.
Increases in the lowest-income quintile's income get the most weight because these households are the poorest. This is the target group of efforts towards poverty alleviation. The second quintile also gets a significant weight because these households also have lower standards of living then most, and are secondary targets of the poverty alleviation plan. The other quintiles also get some weight because increases in these households' income might help poverty alleviation indirectly, for example by creating employment opportunities, creating demand for local products, and raising government tax revenue than can be used for poverty alleviation.
(B.2.e) (2 pts.) For the situation described in part (B.2.a), calculate the numerical value of your ACWI that you constructed in part (B.2.d).
ACWI = 0.1(10%) = 1%, or 0.01
(B.2.f) (2 pts.) For the situation described in part (B.2.b), calculate the numerical value of your ACWI that you constructed in part (B.2.d).
ACWI = 0.5(10%) = 5%, or 0.05
B.3 (B.3.a) (10 pts.) What are the key assumptions of the Lewis model that give rise to its conclusions?
See textbook, pages 108-111, and old midterm answer key.
(B.3.b) (10 pts.) Draw the set of four diagrams typically used to illustrate the
Lewis model, labeling the diagrams in detail. (Please use the scratch paper at the end of this exam.)
See textbook, page 110.

SECTION C: (20 points) You must answer the question in this section.
C.1
Production function: Y = K
α
(AL) 1-α
Assume constant returns to scale (CRS): γY = F(γK, γAL), i.e. if each input (capital and effective labor) is multiplied by some positive real number γ, then output multiplies by γ.
Assume that capital depreciates at rate δ, the labor force (L) grows at rate g
L
, and the productivity of labor (A) grows at rate g
A
.
Assume that fraction s of output is saved, and that all savings are invested (i.e. spent on new capital).
(C.1.a) (4 pts.) Defining y as Y/AL, and k as K/AL, solve for y as a function of k.
See answer key to problem set 2.
(C.1.b) (8 pts.) Solve for Δk (i.e., change in k) as a function of k. Indicate which part of the expression is actual investment per effective worker, and which part is the level of investment per effective worker that would hypothetically keep k constant.
See answer key to problem set 2.
(C.1.c) (4 pts.) In the steady state (i.e., the state when k and y are constant), what determines the growth rate of the capital to labor ratio (K/L) and the growth rate of output per worker (Y/L)? Show this algebraically.
See answer key to problem set 2.
(C.1.d) (4 pts.) If you were a high-ranking member of a developing country's government, what policy lessons might you infer from your answer to part
(C.1.c)?
Open question. Answers might include policies aimed at spurring research and/or adoption of new technologies, or dismantling political barriers to technology adoption.