Eco exam

Problem Set 2

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April 13th

1. Consider a small economy in which consumers only consume apples and bananas. In year

1, qA1 apples and q B 1 bananas are consumed. The price of apples in year 1 is p

A 1 and of

bananas pB1 . The quantities and prices for subsequent years are analogous, as described

in the following table.

Apples Bananas

Quantity Price Quantity Price

1 qA1 p A 1 q

B 1 p

B 1

2 qA2 p A 2 q

B 2 p

B 2

3 qA3 p A 3 q

B 3 p

B 3

Take year 1 as the base year for all calculations.

(a) Which quantities or prices in the above table are irrelevant for the calculation of CPI

in years 1-3 (for example: qA6 , p A 6 , q

B 6 and p

B 6 )?

(b) Which quantities or prices in the above table are irrelevant for the calculation of

nominal GDP in years 1-3?

(c) Which quantities or prices in the above table are irrelevant for the calculation of real

GDP in years 1-3?

(d) Which quantities or prices in the above table are irrelevant for the calculation of

GDP deflator in years 1-3?

2. Consider a small economy in which the representative consumer eats only cheese and

drinks only wine.

1

Cheese (pounds) Wine (bottles)

Quantity Price Quantity Price

2000 1,200 $1.00 40 $10

2001 1,300 $1.20 60 $12

2002 700 $2.00 120 $4

(a) Calculate CPI for all three years, using the complete quantities in 2000 as the rep-

resentative basket.

(b) Does the CPI in 2001 suffer from substitution bias? If so, does this bias overestimate

or underestimate inflation?

(c) Does the CPI in 2002 suffer from substitution bias? If so, does this bias overestimate

or underestimate inflation?

(d) Suppose that the representative consumer has a utility function u(qc, qw) = q 2 c · qw,

where qc is the number of pounds of cheese consumed in a year and qw the number

of bottles of wine consumed. Show that in 2002 the consumer is actually better off

in terms of utility and spends less money by consuming the 2002 quantities of cheese

and wine compared to the 2000 quantities.

(e) Show that GDP deflator is a better representative for 2002 price level than CPI in

light of part (d).

3. Esmerelda entered the labor force in 2000. A shrewd negotiator, her employer agreed to

pay her $10.00 per hour in 2000, and guaranteed a 10% raise in her real wage every year,

indexed to inflation. Using the CPI values you calculated in 2(a) above, what will be

Esmerelda’s nominal wage in 2001 and 2002?

4. (a) Suppose that the nominal interest rate is 6% and inflation is 1%.

i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(b) Suppose that the nominal interest rate is 10% and inflation is 5%.

i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(c) Suppose that the nominal interest rate is 15% and inflation is 10%.

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i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(d) How do the approximate estimates of the real interest rate vary with nominal interest

and inflation rates?

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