# Instructor: Gul Andaman

Macroeconomics I

Instructor: Gul Andaman

BSc II, Section B

Problem Set 1 – Suggested Solutions

Any queries relating to the solutions can be emailed or discussed right before the quiz

1.  Use the supply and demand model to explain how a fall in the price of frozen yogurt would affect the price of ice-cream and the quantity of ice-cream sold. In your explanation, identify the exogenous and endogenous variables.

We can use a simple variant of the supply-and-demand model for pizza to answer this question. Assume that the quantity of ice cream demanded depends not only on the price of ice cream and income, but also on the price of frozen yogurt: Qd = D(PIC, PFY, Y).

We expect that demand for ice cream rises when the price of frozen yogurt rises, because ice cream and frozen yogurt are substitutes. That is, when the price of frozen yogurt goes up, I consume less of it and, instead, fulfill more of my frozen dessert urges through the consumption of ice cream.

The next part of the model is the supply function for ice cream, Qs = S(PIC). Finally, in equilibrium, supply must equal demand, so that Qs = Qd. Y and PFY are the exogenous variables, and Q and PIC are the endogenous variables. Figure 1–1 uses this model to show that a fall in the price of frozen yogurt results in an inward shift of the demand curve for ice cream. The new equilibrium has a lower price and quantity of ice cream.

2.  How often does the price you pay as fee per course change? What does your answer imply about the usefulness of market-clearing models for analyzing the market for education?

The fee per course changes rather infrequently. From casual observation, institutions tend to charge the same price over a one- or two-year period irrespective of the demand or the supply of students and teachers. A market-clearing model for analyzing the market for education has the unrealistic assumption of flexible prices. Such an assumption is unrealistic in the short run when we observe that prices are inflexible. Over the long run, however, the price of courses does tend to adjust; a market-clearing model is therefore appropriate.

3.  Find the data on GDP and its components, and compute the percentage of GDP for the following components for year 2002 onwards.

1. Personal consumption expenditure
2. Gross private domestic investment
3. Government purchases
4. Net exports
5. Imports

Do you see any stable relationship in the data? Do you see any specific trends?

Please note that there is no right or wrong answer to the question. Following graphs show the trends of the mentioned variables. It is up to the understanding of the students how the data points are analyzed. Students will earn marks if the recession period of 2008 – 09 is compared with the growth period of 2002 – 2006

4.  Consider an economy that produces and consumes bread and automobiles. In the following table are data for two different years.

2000 / 2010
Price of an automobile / 400, 000 / 650, 000
Price of a loaf of bread / 12 / 27
Number of cars produced / 100 / 200
Loaves of bread produced / 500000 / 400000
1. Using the year 2000 as the base year, compute the following statistics for each year: nominal GDP, real GDP, the implicit price deflator for GDP and a fixed weight price index such as the CPI.

Year 2000

Nominal GDP: 400,000 * 100 + 500000 * 12 = 40000000 + 6000000 = 46,000,000

Real GDP: (the same) = 46,000,000

GDP Deflator = 100

CPI = Cost of basket of goods in current year/cost of basket of goods in base year = (12 x 500000 + 400000 x 100)/ (12 x 500000 + 400000 x 100) * 100 = 100

Year 2010

Nominal GDP: 650,000 x 200 + 27 * 400000 = 130000000 + 10800000 = 140, 800, 000

Real GDP: 200 x 400000 + 400000 x 12 = 80000000 + 4800000 =

84, 800, 000

GDP Deflator: 140800000/84800000 = 1.66 OR 166

CPI: (650000 x 100 + 500000 x 27) / (100 x 400000 + 12 x 500000) = 78500000/46000000 = 1.70 OR 170

1. How much have prices risen between year 2000 and year 2010? Compare the answers given by Laspayers and Paasche price indices. Explain the difference.

The implicit price deflator is a Paasche index because it is computed with a changing basket of goods; the CPI is a Laspeyres index because it is computed with a fixed basket of goods. From above, the implicit price deflator for the year 2010 is 1.66, which indicates that prices rose by 66 percent from what they were in the year 2000. The CPI for the year 2010 is 1.7, which indicates that prices rose by 70 percent from what they were in the year 2000. If prices of all goods rose by, say, 50 percent, then one could say unambiguously that the price level rose by 50 percent. Yet, in our example, relative prices have changed, making bread relatively more expensive. As the discrepancy between the CPI and the implicit price deflator illustrates, the change in the price level depends on how the goods’ prices are weighted. The CPI weights the price of goods by the quantities purchased in the year 2000. The implicit price deflator weights the price of goods by the quantities purchased in the year 2010. The quantity of bread consumed was higher in 2000 than in 2010, so the CPI places a higher weight on bread. Since the price of bread increased relatively more than the price of cars, the CPI shows a larger increase in the price level.

1. Which measure will you use to adjust and offset changes in the cost of living?

There is no clear-cut answer to this question. Ideally, one wants a measure of the price level that accurately captures the cost of living. As a good becomes relatively more expensive, people buy less of it and more of other goods. In this example, consumers bought less bread and more cars. An index with fixed weights, such as the CPI, overestimates the change in the cost of living because it does not take into account that people can substitute less expensive goods for the ones that become more expensive. On the other hand, an index with changing weights, such as the GDP deflator, underestimates the change in the cost of living because it does not take into account that these induced substitutions make people less well off.

5.  Abby consumes only apples. In year 1, red apples cost \$1 each, green apples cost \$2 each, and Abby buys 10 red apples. In year 2, red apples cost \$2, green apples cost \$1, and Abby buys 10 green apples.

1. Compute CPI of apples for year 2, assuming year 1 is base year.

The consumer price index uses the consumption bundle in year 1 to figure out how much weight to put on the price of a given good: According to the CPI, prices have doubled.

1. Compute Abby’s nominal spending on apples in each year. How does it change from year 1 to year 2?

Nominal spending is the total value of output produced in each year. In year 1 and year 2, Abby buys 10 apples for \$1 each, so her nominal spending remains constant at \$10. For example,

1. Using year 1 as base year, compute Abby’s real spending on apples in each year. How does that change from year 1 to year 2?

Real spending is the total value of output produced in each year valued at the prices prevailing in year 1. In year 1, the base year, her real spending equals her nominal spending of \$10. In year 2, she consumes 10 green apples that are each valued at their year 1 price of \$2, so her real spending is \$20. That is,

1. Compute the GDP deflator in each year and analyze it.

The implicit price deflator is calculated by dividing Abby’s nominal spending in year 2 by her real spending that year:

Implicit Price Deflator2 = Nominal Spending / Real Spending

= 20 / 10

= 0.5.

Thus, the implicit price deflator suggests that prices have fallen by half. The reason for this is that the deflator estimates how much Abby values her apples using prices prevailing in year 1. From this perspective green apples appear very valuable. In year 2, when Abby consumes 10 green apples, it appears that her consumption has increased because the deflator values green apples more highly than red apples. The only way she could still be spending \$10 on a higher consumption bundle is if the price of the good she was consuming fell.

6.  Increases in real GDP are often interpreted as increases in welfare. What are some of the problems with this interpretation? Which do you think is the biggest problem with it and why?

GDP doesn’t take into account the welfare increases due to the value added by the provision of housing services or better quality of goods rather than the quantity of goods and services produced and includes only approximated imputed values (such as environmental degradation, underground economy, value of government services, etc). If real GDP is increasing at the expense of per capita GDP growth rate, environmental conditions and quality of the goods, then welfare is actually falling. Hence GDP values are just the reference points which are analyzed in conjunction with other welfare measures such as Human Development Index, and Gini coefficient.

7.  What is the GDP deflator, and how does it differ from CPI and PPI? Under what circumstances might it be a useful measure (give two scenarios) of price than CPI and PPI?

It is a widely used measure of inflation calculated as the ratio of Nominal GDP to Real GDP. The differences should be discussed in terms of:

a. Nature of goods used in the measurements of CPI, PPI and GDP Deflator

b. Weights attached to goods (changing in GDP Deflator and constant in CPI)

c. Imported goods and their prices subtracted from GDP Deflator calculations and included in CPI

It will be a better measure than CPI if people have the option of substituting to less expensive products as a result of higher prices. Secondly, if price rise of ‘wider group of goods produced locally’ has to be measured, then GDP deflator would be a better indicator.

8.  If you woke up in the morning and found out that nominal GDP had doubled overnight, what statistic you need to check before you began to celebrate? Why?

Nominal GDP can increase because of higher prices or higher output or both while real GDP increases only because of higher output at the base prices. We need to check the real output statistic. If it has increased too, then the real growth has taken place.

9.  Suppose you make a loan of \$100 that will be repaid to you in 1 year. If the loan is denominated in terms of a nominal interest rate, are you happy or sad if inflation is higher than expected during the year? What if the loan instead was denominated in terms of real return?

If inflation is higher than the expected inflation, then the value of the loan paid back would be lower. The lender will lose and the borrower will win, transferring the purchasing power from the lender to the borrower. If the loan was denominated in terms of real interest rate, then the arbitrary redistribution of wealth won’t take place.

10.  Show from national income accounting that

1. An increase in taxes (while transfers remain constant) must imply a change in net exports, government purchases, or the saving-investment balance

S – I = (G + TR – TA) + NX

TA = G + TR + NX + I – S

If taxes increase, then the other side of the equation must change too. With Transfers constant, the change must be a higher G, higher NX, higher I or lower S.

b.  An increase in disposable income must imply an increase in consumption or an increase in saving

YD = S + C à if disposable income increases, the change could be saved or consumed.

c.  An increase in both consumption and saving must imply an increase in disposable income.

This is consistent with the equation above.

11.  Refer to the following information:

GDP: \$6000

Gross investment: 800

Net investment: 200

Consumption: 4200

Government purchases: 1100

Government Budget Surplus: 30

What is

a.  NDP? = 6000 – (800 – 200) = 5400

b.  Net exports? = 6000 – 800 – 4200 – 1100 = – 100

c.  Government taxes – transfers? à BS = TA – G – TR à 30 = TA – 1100 – TR à TA – TR = 1130

d.  Disposable personal income? Y – TA + TR = 6000 – 1130 = 4870

e.  Personal saving? = 4870 – 4200 = 670

12.  Consider an economy that consists only of those who bake bread and those who produce its ingredients. Suppose that this economy’s production is as follows: 1 million loaves of bread (sold at \$2 each); 1.2 million pounds of flour (sold at 1\$ per pound); and 100000 pounds each of yeast, sugar and salt (all sold at \$1 per pound). The flour, yeast, sugar and salt are sold only to bakers, who use them exclusively for the purpose of making bread.

1. What is the value of output in this economy (that is, nominal GDP)?

Expenditure approach: 1000000 x 2 = \$2000000

1. How much value is added to the flour, yeast, sugar and salt when the bakers turn them into bread?

Value added to flour: 1.2 million x 1 = \$1200000

Value added to other ingredients: 100000 x 3 x 1 = \$300000

13.  Suppose a country’s CPI increased from 2.1 to 2.3 in the course of one year. Use this fact to compute the rate of inflation for that year. Why might the CPI overstate the rate of inflation?

(2.3 – 2.1)/2.1 * 100 = 9.52%

As prices increase, people substitute to less expensive goods or locally produced goods. Since the basket of goods is not changed or updated (that can include imported goods too), the cost of living is overstated.