Eco exam

Problem Set 3

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April 20th

1. (a) Discuss the six sources of economic growth and give an example of each.

(b) Suppose that population grows at a rate of 1% per year and the share of the popu-

lation with jobs levels out to 45%.

i. If GDP remains constant, what will be the growth rate of GDP per capita?

ii. What would the growth rate of GDP need to be for GDP per capita to remain

constant?

iii. What would the growth rate of GDP need to be for GDP per capita to increase

by 1% each year?

2. (a) Using the “years to double” shortcut, find the number of years one dollar takes to

double in value if it earns compound interest at a rate of: (i) 2%, (ii) 4%, (iii) 7%,

and (iv) 9% (years need not be whole numbers).

(b) Using the exact compound interest calculation, find the multiple by which each dollar

actually increases in (i)-(iv) in the number of years the shortcut implies (e.g. for

10% each dollar increases by a factor of 1.986). Does our shortcut provide a good

estimate? For which rate is it most accurate?

(c) Can you come up with a “years to triple” shortcut?

3. Suppose country A has grown its GDP at a rate of 2% over the past 30 years. Country

B, on the other hand, has only grown at a rate of 0.5% over the past 30 years.

(a) What are some reasons that country B might be experiencing a slower rate of growth

over this 30 years?

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(b) If the countries start with the same GDP, how much larger (as a percentage) is the

GDP of country A after 30 years than that of country B?

(c) Suppose country B transitions to a free-market economy with well-defined property

rights and as a result, its growth rate increases. If country A continues to grow at

a rate of 2% per year, what must be the rate of growth for country B if its GDP

catches up to that of country A after another 30 years?

(d) Now 60 years have passed and the countries have the same GDP. What if the growth

rates in (c) continue for another 30 years? Whose GDP will by larger and by what

percentage?

4. Suppose Robert is a taxi driver and is considering starting his own business. It costs

$10,000 to buy a taxi, and Robert is willing to use his savings of $5,000 to pay for the car.

He can borrow or lend any amount at an interest rate of 5%. Based on his experience

with driving, Robert expects that for each hour he works, he will earn in taxi fares:

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$19 $23 $21 $20 $19 $18 $17 $15 $13 $12

Moreover, he anticipates using one gallon of gas per hour and the cost of gas is $3.00 per

gallon. Robert places a value of $13 per hour on his leisure time, meaning he will not

work for any hourly rate lower than that.

Alternatively, Robert can continue working for a large livery business where he earns $540

per week and does not pay for any of the car’s expenses.

Assume Robert would work 5 days per week at either job.

(a) If Robert were to buy a car, how many hours per day would he drive it and what

would be his daily profit?

(b) Assume that Robert must pay the loan off plus the 5% interest after 52 weeks. Also

assume that after 52 weeks he can sell the car for exactly what he paid for it, $10,000.

If the hours worked are the same either way, would Robert buy the car and start his

own business or continue working at his current job?

(c) If the car depreciated at a rate of 10% per year, would Robert still start his own

business?

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(d) At what rate of depreciation would Robert be indifferent between starting his own

business or continuing his current job?

(e) Suppose again that depreciation is 10%. If the interest rate at which Robert can

borrow or lend were instead 10%, would he start his own business?

(f) With 10% depreciation, at what rate of interest would Robert be indifferent between

starting his own business or continuing his current job?

(g) If Robert were to buy a car and gas prices rose to $4.50 per gallon, how many hours

per day would he drive and what would be his daily profit?

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