BHWK

Econ 333, Spring 2020 (100 pts) ANSWERS

Midterm Exam

Test Questions

1. (4 pts) A country produces only T-shirts and restaurant meals as final goods and services. It also produces thread that is used entirely to make the T-shirts. It produces 100 T-shirts, 200 units of thread, and 300 restaurant meals in a year. The T-shirt price is $20, the thread price is $5, and the restaurant meal price is $50 in this year. What is the country’s GDP for this year? Show your work.

GDP = 100Tshirts*$20 + 300meals*$50 = $17,000

Only final goods are included in GDP to prevent double counting the intermediate goods. Thread is an intermediate good so it is not included (it’s value is already included in the T-shirts!).

2. Country Z’s GDP/capita in 2015 is 9,000 Zfrancs. Suppose in 2015 a representative basket of goods and services costs 3000 Zfrancs in Country Z. The same basket of goods and services costs $5000 in the US in US dollars.

2a. (4 pts) Using this information, calculate the PPP exchange rate for Country Z? Show your work. Make sure to include currency units (don’t just give a number)

PPP exchange rate = 3000ZFrancs/5000$ = .6 Z Francs/ 1$

I also gave credit if this was given as 1.67 $/ 1 ZFranc

2b. (4 pts) If the PPP international extreme poverty line in international dollars is PPP$1.90 per day per person, what is this poverty line in terms of Z francs? Show your work.

PPP $1.90 * .6Zfrancs/1$ = 1.14 ZFrancs

1.14 ZFrancs = the international extreme poverty line in Country Z.

2c. (4 pts) Now consider Country X. Suppose the international extreme poverty line of PPP$1.90 per day per person converts to 5000Shillings per person per day in Country X using the PPP exchange rate for Country X. What can you say about similarity or differences in purchasing power of 5000 Shillings per person per day in Country X and the poverty line amount of Zfrancs you calculated in question 2b? This should be a one or two sentence answer.

This question is asking about the purchasing power of 5000 Shillings and 1.14 ZFrancs, i.e., the extreme poverty income/consumption amount per person per day. Since they are converted with their respective PPP exchange rates, they should both have the same purchasing power. And their purchasing power is also equal to $1.90.

3. (10 pts) Use the index formula covered in class for this question. Consider an index for PPP GDP per capita calculated with data from all countries in the world. Suppose the minimum and maximum PPP GDP/cap values used in calculating the index are determined by the actual minimum and maximum values observed in that year in the distribution of country PPP GDP/caps.

We observe that for Country A the PPP GDP/cap index value decreases from one year to the next. Can we conclude that the PPP GDP per capita in Country A has necessarily decreased? Provide a proof of your answer. You can use made up numbers in the proof to make your point.

Index Formula for country A = (YA – Ymin) / (Ymax – Ymin)

Where here Y is PPP GDP per capita.

No, we cannot conclude that if Country A’s index value decreases that Country A’s PPP GDP per capita has decreased.

Proof. Suppose we know

PPP GDP/cap (initial) PPP GDP/cap (I year later)

Max PPP GDP/cap country 200 300

Min PPP GDP/cap country 50 50

Country A 100 100

Country A’s index value 0.33 0.20

Country A’s index value went down although it’s PPP GDP/cap did not change. Mathematically this is because when the Max PPP GDP/cap country’s value went up, that increased the denominator of the index equation, lowering the value of the whole equation. One can also show Country A’s index value will go down if the Min PPP GDP/cap country’s value goes up (that changes both the numerator and the denominator, but the combined effect will be a decrease in Country A’s index value. The conceptual explanation for this mathematical outcome is that in this case Country A’s value is showing its position relative to the overall distribution of PPP GDP/cap in the sample of countries. Specifically, it’s relative to the max and min values.

Note: we cannot say that, for example in the initial year, Country A has income higher than a third (.33) of the sample countries. This isn’t a cumulative distribution type measure. Lots of countries could have .33 as their index value! This index measure how far a country is away from the minimum value as a percentage of the maximum observed distance from the minimum value.

4. There are 10 people in a province. The absolute poverty line, z, is 10. You know everyone’s incomes from the table below. I have listed them in order from least income to highest income.

Person ID	Income (Yi)	=1 if Yi< 10	Poverty Gap	Cash Transfer	Poverty Gap	Econ Growth	=1 if Yi< 10
1	3	1	7	6	4	6	1
2	3	1	7	6	4	6	1
3	6	1	4	6	4	12
4	7	1	3	7	3	14
5	11			11		22
6	12			12		24
7	13			13		26
8	13			13		26
9	16			16		32
10	16			16		32
Summed	100	21	21		15	200

4a. (16 pts) A cash transfer program in this province doubles incomes for the lowest quintile in the population. It does not raise anyone else’s income. Sticking with an absolute income-based poverty measure, explain how using 2 different poverty index measures will give you a deeper understanding of whether this program reduces poverty than using just one. You must provide a clearly written explanation. You must also provide relevant numerical calculation of 2 different poverty index measures using the income information in the table and this question, explain what the index measures you are calculating are, and interpretation of the index values you have calculated. Incorporate what you calculate and its explanation as evidence you use to support your points in your written answer to this question.

For quick reference here is the equation for the Foster-Greer-Thorbecke class of poverty index measures. FGTα =

The FGT Headcount Index (initial) (α=0) = 4/10 = 40%. This mean’s 40% of the population has income under the poverty line. So this measure says there are 40% of the population is in poverty.

The FGT Headcount Index (with cash transfer) (α=0) = 4/10 = 40%. This means there are still 40% of the population in poverty (i.e., with incomes under the poverty line).

This poverty measure indicates that poverty did not decrease with the cash transfer. Note, however, that this does NOT mean that this measure does not tell us anything, or that it’s worthless. It does in fact tell us something. It tells us that even with the cash transfer we still have 40% of the population with incomes less than 10.

The FGT Poverty Gap Index (initial) (α=1) = summed pov gaps/max possible summed gap = .21

The FGT Poverty Gap Index (with cash transfer) (α=1) = .15

The Poverty Gap index tells us what proportion of the maximum possible total poverty gap the current actual total poverty gap in the population is. It is a measure of the depth of poverty. By this measure poverty decreased.

Using these two poverty measures together gives us a more complete picture of the effect of the cash transfer program. Using only the Headcount Index we would not see that the depth of poverty in the population decreased with the program. Note also, that using only the Poverty Gap Index would also give us an incomplete picture. Without also knowing the Headcount Index, we wouldn’t know if the Poverty Gap Index decreased because of having less people under the poverty line, or because those under the poverty line are closer to it, or some combination of the two. Since we know the Headcount Index here did not change, we know the Poverty Gap Index decrease was entirely from poor people having incomes closer to the poverty line.

So, using both measures, we can say 40% of the population is still poor, but they are not as deeply poor as they used to be.

Note: Some answers used the Squared Poverty Gap Index (α=2) instead of the Poverty Gap Index. This was fine. The explanation of why using 2 measures gives a more complete picture still holds.

The FGT Poverty Gap Index (initial) (α=1) = .123

The FGT Poverty Gap Index (with cash transfer) (α=1) = .057

4b. (16 pts) Suppose instead of the cash transfer program from part a. there is robust economic growth that doubles everybody’s income. Explain in some detail how two people looking at these same data, and only using these data, can come to two different conclusions to the following question: If everyone’s income doubles will poverty decrease (i.e, one will be yes it does, and another no it doesn’t)? You must define the concepts you use, and also explicitly use the data given to support your explanation.

If one uses an absolute poverty measure, then poverty will be shown to decrease. An absolute poverty measure uses an absolute poverty line, one that is a fixed standard. In our example the absolute poverty line is 10. In this case, the Headcount Index drops from H1 = .40 to H2 = .20 (before the econ growth there were 4 people with incomes under 10 and after economic growth there were 2). So with the absolute measure, poverty falls.

If one uses a relative poverty measure, then poverty will be shown to not have changed. A relative poverty measure uses a relative poverty line, one that changes to keep in the same relative position to incomes in the income distribution. A relative poverty line will increase in our case here. For example, let’s say that the relative poverty line is 10% of the Total Income in the population. Before economic growth, total income is 100 and the relative poverty line is 10% of 100 or 10. With this relative poverty line of 10 the Headcount index = 4/10=.4 or 40% of the population (one can calculate FGT poverty indexes with a relative poverty line just like with an absolute poverty line). With economic growth, the relative poverty line will increase. Total income in the population is now 200, and 10% of 200 is 20. So the new relative poverty line is 20. Headcount index = 4/10=.4 or 40% of the population. Poverty by this relative measure did not decrease (nor would either of the poverty gap measures).

Note: A measure of inequality is NOT a poverty measure, not even a relative poverty measure.

4c. (4 pts) What happens to the Gini coefficient with each of the two scenarios (cash transfer from a., economic growth from b.). Just say for each if it increases, decreases, or stays the same. Clearly write which answer is for which scenario. Both scenarios entail a large increase in aggregate income.

Cash Transfer: Gini coefficient decreases (because the income increase disproportionately favored the bottom quintile)

Economic Growth: Gini coefficient stays the same (because the relative distribution of incomes did not change-the growth was distribution neutral-and the Gini coefficient is a measure in inequality in the distribution of income, not a measure of relative poverty).

5. Consider the basic Solow model with population growth rate, n, and depreciation, d, and savings rate, s.

5a. (10 pts) Suppose a country is initially at its steady state capital per worker (k*) and output per worker (y*). Illustrate this situation graphically, making sure to label each line you draw with exactly what it is. Label what is measured on the axes too. Clearly label k* and y*.

(n + d)k

y,i (output per worker, investment per worker)

y* y= f(k)

y2*

i = sf(k)

Δk

i’ = s’f(k)

k2* k* k (capital per worker)

5b. (16 pts) Now the country experiences a decrease in its savings rate. Use your graph, and any clearly labeled changes you make to it, to explain what the Solow model predicts will happen to the following 3 things as a result of the savings rate decrease.

1) steady state capital per worker,

2) steady state output per worker, and

3) the country’s long run rate of growth in steady state output per worker

Your written explanation must include an explanation how any dynamic transition occurs (or why there isn’t any). Refer to specific things you label on the graph in your explanation. More complete explanations get more points.

See the graph. With a lower savings rate (s), the i= sf(k) function will shift down. At k* with the new lower amount of saving there is also a new lower amount of investment. Investment is now not enough to cover the required investment, (n+d)k, to keep capital per worker from declining due to the effects of depreciation and population growth. This is what causes capital per worker to decline. On the graph the one period decline in k, Δk , is given by the arrowed line to show the difference between the amount of investment and the amount of required investment. The decline in k will continue until the new steady state capital per worker is reached at k2* where s’f(k) = (n+d)k. At k2* the amount of output per worker is y2*.

So, as a result of the savings rate decrease we predict

Capital per worker will decrease (i.e, from k* to k2*)

Output per worker will decrease (i.e., from y* to y2*)

The country’s long run rate of growth in steady state output per worker will equal zero! Once the new steady state output per worker is reached, there is no more change in output per worker in the Solow model (unless something new and exogenous happens like an increase in technology). Just from the change in the savings rate there is no change in the growth rate of steady state output per worker.

6. (12 pts) Pick ONE of the following two questions to answer. Clearly label which question you are answering as 6A or 6B. If you answer both I will grade 6A. These answers are meant to be about 4 or 5 sentences.

6A. According to Amartya Sen, poverty is defined as deficiency in capabilities to live the life one has reason to value. This contrasts with poverty as deficiency of income. Clearly explain two reasons why it is difficult to make an operational way to measure capability poverty that people will all agree on. Use the OPHI Multidimensional Poverty Index (MPI) as an example to show how these two reasons must be dealt with to create a poverty measure, and how a particular solution could be debatable. (You do not need to provide lots of details about the MPI, just describe it enough to make your points.)

There need to be two reasons why it is difficult to make a capability poverty measure. Some possible reasons that we have covered:

One needs to decide on whether to measure capabilities or functionings, and people can disagree about this.

One needs to decide on which capabilities (or functionings) to include in a capability poverty measure, and people can disagree about this.

One needs to decide what weights to give each included capability (functioning) in the measure, and people can disagree about this.

The OPHI MPI has a specific set of functionings, and clearly expresses the weights given to each included thing. One can argue with the weights given, or that they should have included additional things, or that they should not have included something they did.

6B. In the Solow Growth Accounting (aka Sources of Growth Analysis) framework Total Factor Productivity (TFP) contributes to economic growth. Explain the difference between Proximate and Fundamental sources of economic growth, and how they are related to each other. Also explain what growth of TFP is meant to measure, and where growth of TFP fits within these two concepts.

Proximate sources of economic growth are the sources most close to the actual production of goods and services. These are accumulation of factor inputs (particularly human capital and physical capital), and technological growth that enhances productivity.

Fundamental sources of economics growth are things that influence how well (or not well) an economy can accumulate factor inputs or achieve technological growth. The main contenders these days for Fundamental sources of economic growth are geography and institutions.

Proximate and Fundamental sources of growth are related because the Fundamental sources influence the ability of the economy to have the Proximate sources.

Total Factor Productivity (TFP) is a measure of technology, and growth in TFP is a measure of growth in technology that enhances productivity. So TFP growth is one of the Proximate sources of economic growth.