ECON 102 Tutorial: Week 15

Ayesha Aliwww.lancaster.ac.uk/postgrad/alia10/econ102.html

a.ali11@lancaster.ac.ukoffice hours: 8:00AM – 8:50AM tuesdays LUMS C85

Today’s Outline

Planet Money Podcast – #222 Consumer Price Index Feedback: Did you like the podcast? Was it useful in understanding how we calculate the Consumer

Price Index? Did you find any problems with using the CPI as a measure of

the cost of living?

Week 15 worksheet: Price Index and Inflation Problems: Q1-Q8 Unemployment Problems: Q9-Q14 In class today, we’ll only go through the problems that you have

questions on; otherwise please make sure you review all of problems on your own and ask if you have any questions.

Question 1(a) A government survey determines that typical family expenditures each month in the year designated as the base year are as follows:

• 20 pizzas €10 each• Rent €600 per month• Petrol and car maintenance €100• Phone service €50

In the year following the base year, the survey determines that pizzas have risen to €11 each, rent is €640, petrol and car maintenance have risen to €120 and the phone service has dropped in price to €40.

Find the CPI in the subsequent year.

Question 1(a) ctd. Find the rate of inflation between the base year and the subsequent year.

We know the CPI in the base year is 1.0 and we just found the CPI for the following year is 1.074. We need to find the rate of inflation between these two years.

The rate of inflation is equal to the percentage change in prices, in this case, measured by the CPI.

In general, when calculating inflation, we simply use the previous year as the base year, unless we specify otherwise. You’ll see this in later problems, where in some questions we are just told to calculate the rate of inflation (which means using the previous year as base year) and in other questions we are told to calculate rate of inflation with a specific year as the base year.

Question 1(b) The family’s nominal income rose by 5 per cent between the base year and the subsequent year. Are they worse off or better off in terms of what their income is able to buy?

To answer this question, we should compare the change in the family’s nominal income to the change in the cost of living, or the inflation rate.

We know that the family’s nominal income rose by 5%.And we calculated the inflation, which is 7.4%

So, the rise in the family’s nominal income is less than the increase in the cost of living; that means that the family is worse off, in terms of real purchasing power.

Question 2 The table below gives the HICP for the Euro Area for each year from 1999 to 2010. For each year, beginning with 2000, calculate the rate of inflation from the previous year. What happened to inflation rates between 1999 and 2010?

So, to calculate the rate of inflation from the previous year, we’ll need that equation for inflation.

Year HICP1999 87.622000 89.542001 91.712002 93.782003 95.782004 97.872005 100.002006 102.202007 104.392008 107.832009 108.152010 109.87

Year HICP Inflation Calculation Inflation Rate1999 87.622000 89.542001 91.712002 93.782003 95.782004 97.872005 100.002006 102.202007 104.392008 107.832009 108.152010 109.87

𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛𝑅𝑎𝑡𝑒=𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑦𝑒𝑎𝑟 𝑝𝑟𝑖𝑐𝑒𝑠−𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟 𝑝𝑟𝑖𝑐𝑒𝑠

𝐵𝑎𝑠𝑒 𝑦𝑒𝑎𝑟 𝑝𝑟𝑖𝑐𝑒𝑠×100

Question 2 The table below gives the HICP for the Euro Area for each year from 1999 to 2010. For each year, beginning with 2000, calculate the rate of inflation from the previous year. What happened to inflation rates between 1999 and 2010?

In most years between 1999 and 2010 the yearly inflation rate was close to 2%. But in 2008 the rate rose to above 3% and then dropped to close to 0% in the following year (2009).

Year HICP100 x (current year HICP - prev.

year HICP) / prev. year HICP Inflation rate

1999 87.622000 89.54 100 x (89.54 – 87.62) / 87.62 2.19%2001 91.71 100 x (91.71 – 89.54) / 89.54 2.42%2002 93.78 2.26%2003 95.78 2.13%2004 97.87 2.18%2005 100.00 2.18%2006 102.20 2.20%2007 104.39 2.14%2008 107.83 3.30%2009 108.15 0.30%2010 109.87 1.59%

Question 3(a) The typical consumer’s food basket in the base year 2000 is as follows:

30 chickens @ €3.00 each 10 hams @ €6.00 each 10 steaks @ €8.00 each A chicken feed shortage causes the price of chickens to rise to €5.00 each in 2001. Hams rise to €7.00 each, and the price of steaks is unchanged.

Calculate the change in the ‘cost-of-eating’ index between 2000 and 2001.

This is just another price index, like CPI, so we do the same steps as in Q1.

So the official “cost of eating” index is: In 2000, the cost is €90 + €60 + €80, or €230. In 2001, the cost is €150 + €70 + €80, or €300.

So the official “cost of eating” has increased by 30.4% between 2000 and 2001.

Question 3(b) The typical consumer’s food basket in the base year 2000 is as follows:

30 chickens @ €3.00 each 10 hams @ €6.00 each 10 steaks @ €8.00 each A chicken feed shortage causes the price of chickens to rise to €5.00 each in 2001. Hams rise to €7.00 each, and the price of steaks is unchanged.

Suppose that consumers are completely indifferent between two chickens and one ham. For this example, how large is the substitution bias in the official ‘cost-of-eating’ index? Since two chickens now cost more than one ham and people are indifferent between 2 chickens and 1 ham, they will switch from 30 chickens to 15 hams, so that total ham consumption will be 25. The cost of the food basket is now 25 hams at €7.00 plus 10 steaks at €8.00, or €255. The true increase in the cost of eating is (€255 - €230)/€230, or 10.9%, much lower than the official estimate (in part a) of 30.4%.

The overestimate of inflation in the cost of eating reflects substitution bias.

Question 4 Joe starts a new job in January 2009 at an annual salary of €30,000. At the end of the year Joe

gets a 5% pay rise. The CPI is 110 in 2009 and 114.3 in 2010.Calculate the percentage change in Joe’s real income over 2009 – 2010. So first, let’s find Joe’s Real Income in 2009 and 2010, and then let’s find the percentage change.

In order to find real income in a given year, we need to take nominal income divided by the price index for that particular year. (just like we did with real and nominal GDP last week)

His nominal income in 2010 is 5% higher than in 2009, so it is €30,000 x 1.05 or €31,500.

Now that we have his Real Income in both years, we have enough information to find the percentage change in real income.

Question 4 So how can we find the percentage change in Joe’s Real income between 2010 and 2009?

In general terms, a percentage change is:

So Joe’s percentage change in real income would be:

Alternatively, this percentage change in real income could also have been calculated from nominal pay rise (5%) minus the CPI inflation rate. The inflation rate is 100 x (114.3-110)/110 i.e. 3.9%.If we subtract this from his nominal pay raise, we’d have: 5% - 3.9% = 1.1%.

Question 5 Jane, a U.S. citizen, works for a multinational company. She is currently based in London earning a salary of €100,000 per year. Jane’s boss wants her to move to a similar job in Brussels but can only offer a salary of €80,000. Research shows that for expatriates the cost of living is 40 percent higher in London than in Brussels. If Jane accepts the offer would she be better or worse off in terms of her real income? Jane’s nominal salary in London is 25% higher than in Brussels:

100 x (€100,000 - €80,000)/ €80,000

But because the cost of living is also 40% higher in London, Jane’s real income is lower in London than in Brussels, by 25% - 40% i.e. -15%.

Jane would, therefore, be better off in Brussels.

Question 6 On 1 January 2007, Albert invested €1,000 at 6 per cent interest per year for three years. The CPI on 1 January 2007 stood at 100. On 1 January 2008, the CPI stood at 105. On 1 January 2009, it was 110 and on 1 January 2010, the day Albert’s investment matured, the CPI was 118. Find the real rate of interest earned by Albert in each of the three years and his total real return over the three-year period. Assume that interest earnings are reinvested each year and earn interest.

Question 6 On 1 January 2007, Albert invested €1,000 at 6 per cent interest per year for three years. The CPI on 1 January 2007 stood at 100. On 1 January 2008, the CPI stood at 105. On 1 January 2009, it was 110 and on 1 January 2010, the day Albert’s investment matured, the CPI was 118. Find the real rate of interest earned by Albert in each of the three years and his total real return over the three-year period. Assume that interest earnings are reinvested each year and earn interest. First, calculate inflation for each year. Inflation is the percentage increase in the CPI over that year For 2007, inflation is (105–100)/100 = 5%. For 2008, inflation is (110-105)/105 = 4.8%. For 2009, inflation is (118-110)/110 = 7.3%. Real return equals the nominal interest rate minus the inflation rate. Subtracting the inflation rate for each year from the nominal interest rate (6% in each year) gives real returns of 1% in 2007, 1.2% in 2008, and –1.3% in 2009. Now consider the three-year period as a whole. At the end of one year, Albert’s €1000 is worth €1000 x 1.06 = €1060. Assuming that interest is re-invested, at the end of two years he has €1060 x 1.06 = €1123.60, and at the end of three years he has €1123.60 x 1.06 = €1191.02, for a total nominal gain of 19.1% i.e. (€1191.02 - €1000)/ €1000. As the price level has risen by 18% over the three years i.e. (118-100)/100, Albert’s total real return over the three years is 19.1% - 18% = 1.1%.

Question 7(a) Frank is lending €1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a 2 per cent real return per year.

The CPI is 100 at the time that Frank makes the loan. It is expected to be 110 in one year and 121 in two years. What nominal rate of interest should Frank charge Sarah?

Inflation is expected to be (110-100)/100 = 10% in the first year and (121-110)/110 = 10% in the second year.

If Frank charges Sarah a 12% nominal interest rate, he will earn a real return of 2% per year (12% nominal interest rate – 10% inflation rate).

Question 7(b) Frank is lending €1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a 2 per cent real return per year.

Suppose Frank and Sarah are unsure about what the CPI will be in two years. Show how Frank and Sarah could index Sarah’s annual repayments to ensure that Frank gets an annual 2 per cent real rate of return. Indexing is the practice of increasing a nominal quantity each period by an amount equal to the percentage increase in a specified price index; doing this prevents the purchasing power of the nominal quantity from being eroded by inflation.

To ensure a 2% annual return on the loan, Frank and Sarah should agree that Sara will pay an interest rate in each year equal to 2% plus whatever the inflation rate turns out to be.

For example, if inflation turns out to be 8% during the first year and 10% during the second year, Sarah should pay 10% nominal interest in the first year and 12% in the second year.

Question 8 In the base year for computing the CPI expenditures of the typical consumer break down as follows:

A consumer who spent €100 in the base year would spend €17.80 on food and beverages, €42.80 on housing, €6.30 on apparel and upkeep, and so on. To buy the goods and services this year, which cost €100 in the base year, the consumer would have to increase his spending on food and beverages from €17.80 to €19.58 (a 10% rise), on housing from €42.80 to €44.94, and on medical care from €5.70 to €6.27. Other expenditures would be the same as in the base year. So, the total cost of the basket can be found to be €104.49.The CPI for the current year is 1.0449 or (multiplying by 100), 104.49.

Item %Food and beverages 17.8Housing 42.8Clothing 6.3Transportation 17.2Medical care 5.7Entertainment 4.4Other goods, services 5.8Total 100.0

Suppose that since the base year: the prices of food and beverages have increased by 10% , the price of housing has increased by 5% the price of medical care has increased by 10% Other prices are unchanged.

Find the CPI for the current year.

Question 9(a) The towns of Littlehampton and Bighampton each have a labour force of 1,200 people.In Littlehampton, 100 people were unemployed for the entire year, while the rest of the labour force was employed continuously. In Bighampton every member of the labour force was unemployed for 1 month and employed for 11 months. What is the average unemployment rate over the year in each of the two towns?

In Littlehampton, 100/1200 of the labour force, or 8.3% was unemployed. In Bighampton, each worker is unemployed 1/12 of the time, so the avg. unemployment rate is also 8.3%. (Notice that both Bighampton and Littlehampton experience 100 person-years of unemployment and 1100 person-years of employment.)

Question 9(b) The towns of Littlehampton and Bighampton each have a labour force of 1,200 people.In Littlehampton, 100 people were unemployed for the entire year, while the rest of the labour force was employed continuously. In Bighampton every member of the labour force was unemployed for 1 month and employed for 11 months. What is the average duration of unemployment spells in each of the two towns?

Littlehampton has 100 unemployment spells, each lasting a year, so the average duration of unemployment in Littlehampton is one year. Bighampton has 1200 unemployment spells, each lasting a month, so the average duration of unemployment is one month.

Question 9(c) The towns of Littlehampton and Bighampton each have a labour force of 1,200 people.In Littlehampton, 100 people were unemployed for the entire year, while the rest of the labour force was employed continuously. In Bighampton every member of the labour force was unemployed for 1 month and employed for 11 months. In which town do you think the costs of unemployment are higher? Explain.

Because spells are shorter in Bighampton, the costs of unemployment (particularly the psychological and social costs) are likely to be smaller.

Question 10(a) In a total population of 10 million people 20% are classified as not being of working-age. In the working-age population 40 percent as classified as employed, 20 percent are classified as retired or in full-time education and 10 percent are classified as not seeking employment.

For this population calculate the labour force.

The labour force is the sum of those classified as employed and those classified as unemployed. In the total population of 10 million 20% or 2 million are classified as not being of working-age. That leaves us with 8 million who are of working-age.

Of these 8 million, 40% (or 3.2 million) are classified as employed, 20% (or 1.6 million) are classified as retired or in full-time education and 10% (or 0.8 million) are classified as not seeking employment. That accounts for 70% of the 8 million who are of working-age. So the remainder of the working-age population or 30% of 8 million (or 2.4 million) must be unemployed.

So, The labour force equals the 3.2 employed plus the 2.4 unemployed or 5.6 million.

Question 10(b) In a total population of 10 million people 20% are classified as not being of working-age. In the working-age population 40 percent as classified as employed, 20 percent are classified as retired or in full-time education and 10 percent are classified as not seeking employment.

For this population calculate the unemployment rate.

The unemployment rate = unemployed/labour force = 2.4/5.6 = 0.428 or 42.8%

Question 10(c) In a total population of 10 million people 20% are classified as not being of working-age. In the working-age population 40 percent as classified as employed, 20 percent are classified as retired or in full-time education and 10 percent are classified as not seeking employment.

For this population calculate the labour force participation rate.

The labour force participation rate = labour force/population of working age = 5.6/8 = 0.7 or 70%

Question 11 The US BLS (http://stats.bls.gov) reported the following data (in millions) for January 08 and January 11:

Calculate the labour force, the unemployment rate, and the participation rate for January 2008 and January 2011. How does the latter compare with the former? The labour force is the number of employed and unemployed. 153.8 mil. in Jan 2008 and 153.1 mil. in Jan 2011. The unemployment rate is the number of unemployed divided by the labour force: 7.6 / 153.8 or 4.9% in 2008 and 13.8 / 153.1 or 9.0% in 2011. The participation rate is the labour force divided by the working age population (or the labour force plus the people not in the labour force in the table above). 2008: 153.8 / (153.8 + 78.8) = 66.1%, 2011: 153.1 / (153.1 + 85.5) = 64.2%. So in January 2011, compared to 3 years earlier, the number of unemployed and the rate of unemployed are very much higher. At the same time the labour force has decreased, so a rising number of people have left the labour force altogether, leading to a lower participation rate.

January 2008

January 2011

Employed 146.2 139.3Unemployed 7.6 13.8Not in labour force 78.8 85.5

Question 12(a) The demand for and supply of labour in a certain industry are given by the equations

Nd = 400 – 2w Ns = 240 + 2w

where Nd is the number of workers employers want to hire, Ns is the number of people willing to work, both labour demand and labour supply depend on the real wage w, which is measured in euros per day. Find employment and the real wage in labour market equilibrium.

Equating demand and supply gives: 400 – 2w = 240 + 2w w = 160/4 w = €40

Substituting for w in either the demand or supply equations gives Nd = Ns = 320.

Question 12(b) The demand for and supply of labour in a certain industry are given by the equations

Nd = 400 – 2w Ns = 240 + 2w

Suppose the minimum wage is €50 per day. Find employment and unemployment. Is anyone made better off by the minimum wage? Worse off? In answering the last part of the question, consider not only workers but employers and other people in the society, such as consumers and tax-payers. With a minimum wage = €50 demand is Nd = 400 – 100 = 300 and supply is Ns = 240 + 100 = 340. Hence 340 people are seeking work but only 300 find work at the minimum wage and 40 people are unemployed.

Those employed are better off but those made unemployed are worse off. Consumers will be worse if the higher wage is passed on in terms of higher prices. Tax-payers will also be worse-off as more tax revenue is required to pay unemployment benefits.

Question 12(c) The demand for and supply of labour in a certain industry are given by the equations

Nd = 400 – 2w Ns = 240 + 2w

where Nd is the number of workers employers want to hire, Ns is the number of people willing to work, both labour demand and labour supply depend on the real wage w, which is measured in euros per day. We do the same steps as in part (b), but now assume that a union contract requires workers be paid €60 per day.

With a union wage = €60 demand is Nd = 400 – 120 = 280 and supply is Ns = 240 + 120 = 360.

Hence 360 people are seeking work but only 280 find work and 80 people are unemployed.

Question 13 Use the demand and supply equations in question 12(a). Now suppose that the cost of

complying with new government regulations on workplace safety reduces labour demand to Nd = 360 – 2w.

Find the change in numbers employed and the equilibrium wage, as compared to your answer in 12(a).

First, we set supply equal to demand: 360 – 2w = 240 + 2w w = 120/4

w = €30 Substituting for w in either the demand or supply equations gives Nd = Ns = 300.

So, the equilibrium wage falls by €10 and employment by 20 people.

Question 14 How would each of the following be likely to affect the real wage and employment of unskilled workers on an automobile plant assembly line?a. Demand increases for the type of car made by the plant.

An increase in the demand for cars will lead to an increase in the demand for all workers. Hence the real wage and employment opportunities for unskilled workers will increase.

b. A sharp increase in the price of petrol causes many commuters to switch to public transport.

This is the reverse of part a. A decrease in the demand for cars will lead to a decrease in the demand for all workers. So real wage and employment opportunities for unskilled workers will fall

c. Because of alternative opportunities, people become less willing to do factory work.

As the supply of unskilled workers falls relative to demand (the supply curve shifts to the left) wages will increase and the numbers employed will fall.

d. The plant management introduces new assembly line methods that increase the number of cars unskilled workers can produce per hour while reducing defects.

The new assembly line increases the productivity of unskilled workers (the demand curve shifts to the right) leading to an increase in both wages and employment.

Next Class

Week 16 Worksheet – Economic growth Chapter 20 in your textbook

No Podcast for next week.