# MacroPractice

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## Practice Questions

**Q** In Econland 25% of the 2 million people in the country are employed. Average labour productivity in Econland is $15,000 per worker. Real GDP per person in Econland totals:

**A** Since only 2000000*0.25 = 50000 people are working, the total GDP of the country is 15000*50000. To find GDP per capita, divide the total GDP by the population 2000000. The answer is 3750.

**Q** Assume that an economy has 2,000 workers, each working 4,000 hours per year. If the average real output per worker-hour is $10, then total output or real GDP will be:

**A** With the income approach of calculating GDP, we need to calculate the total amount of income received by the workers, ie, 2000*4000*10 = 80mil.

**Q** three workers run a house painting business and always work the same number of hours together. The paint they use requires applying two coats. Each worker paints 200 square feet per hour using a roller or 80 square feet per hour using a brush. if a technological advance provides a paint that only requires one coat, their average labour productivity per hour as a team: A. will decrease. B may either increase or decreases; C. increase only if they use brushes; D. remain the same; E. increases

**A** The correct answer is "remain the same or increase". The reason is that if the new paint lowers the productivity, the workers will choose NOT to use it. In that case, their average productivity will remain the same. However, if the workers choose to use the new paint, then it must mean that their productivity increases. Therefore it can stay the same or increases. If we are forced to choose, the answer is (E).

However, under the assumption that the workers are forced to use the new paint (I consider this assumption only because the correct answer is not given, so we have to "outguess" this stupid question), then the answer is (B). The reason is that there is not enough information to answer the question. What's missing is the technology that's being used for the two types of paint, so there are scenarios where the productivity would increase, and there are scenarios where it would decrease. For example, if both the old and new paint allow the use of both the roller and the brush, then average productivity increases because the workers only need to paint once with the new paint. However, suppose the new paint can be applied only with a brush but the old paint can be used by both the brush and the roller, then the workers using the new paint can only paint 80 sq ft per hour, less than half of the 200 sq ft per hour they could paint with the old paint.

**Q** If an economy's real GDP doubles in fourteen years, then the average annual rate of growth in real GDP is about:

**A** The rule of 72 says that for GDP (or anything that grows "compoundly"), the number of years it takes to double * growth rate in percentage ~ 72. If the number of years to double is 14, then 72/14 ~ 5 is the growth rate.

**Q** Real GDP per person in the United States was $9,864 in 1950. Over the next 48 years it grew at a compound annual rate of 2.0%. If instead real GDP per person had grown at an average compound annual rate 2.5%, then real GDP per capita in the United States in 1998 would have been how much larger?

**A** We can calculate by the compound interest formula. if it grows at 2%, then it would be 9864(1 + 0.02)^{48} = 25518. if it grows at 2.5%, then 9864(1+0.025)^{48} = 32269. The difference is $6750.

## IS/LM numerical example

ASIMO is a small, closed economy defined by the following equations: C = 300 + 0.8(Y − T) − 500r; I = 400; T = 100; G = 80; Md/P = 0.5Y − 250r; Ms = 10000; Ms = Md; Y = C+I+G Throughout the question, we will limit ourselves to short-run analysis and set P = 10. (a) Find equilibrium Y and r. (b) Suppose the central bank of ASIMO decides to perform an open market purchase of 250 in securities. If the reserve requirement ratio is 0.10, what is the new equilibrium Y and r? (Hint: you only need to redo half of the algebra from part (a).) What happens to the AD curve in this case? (c) Going back to the original set of equations in part (a), suppose the government of ASIMO increases its spending by 100. Find the new equilibrium Y and r. This is related to the “crowding-out effect.” Explain the crowding-out effect. Make sure your answer is specific to the model in this problem.

A. Find equilibrium Y and r. The IS curve is: Y = C + I + G Y = 300 + 0.8(Y − 100) − 500r + 400 + 80 0.2Y = 700 − 500r Y = 3500 − 2500r Set MS = MD implies the LM curve is Md/P = 10000/10 = 0.5Y −250r. It can be rewritten as Y = 2000 + 500r. Combining to get: 2000 + 500r = 3500 − 2500r 1500 = 3000r r = 0.5 Y = 2000 + 500r = 2250

B. An open market purchase of $250 at reserve ratio of 10% would increase the money supply by 250/0.1 = 2500. It would change the LM curve but not the IS curve. Thus the LM curve becomes Y = 2500+500r. Solving yields r = 1/3 and Y = 2667. The above implies an increase in Y while holding the price level constant. Thus the AD curve shifts to the right.

C. The multiplier of government expenditure is 1/0.2 , so the GDP will increase by 100/0.2 = 500, and the IS curve becomes Y = 4000 − 2500r. Solving yields r = 2/3 , and Y = 2333. When government increases spending, it would increase GDP through the multiplier effect. However, the increase in final GDP (2333 - 2250 = $83) is smaller than the increase in GDP due to the multiplier effect alone ($500). The reason is that an increase in GDP leads to an increase in money demand, which drives the interest rate up. In turn, the increased interest rate leads to a decrease in consumption (not investment in this particular question), which lowers the GDP and offsets the effect of the increase in government expenditure. In other words, the government spending crowds out consumption.

## Finance

**Q** You have $2000 to invest and are considering buying some combination of the shares of two companies, LionInc and DonkeyInc. Shares of LionInc will pay a 8 percent return if the Conservatives are elected, an event you believe to have a 40 percent probability; otherwise the shares pay a zero return. Shares of DonkeyInc will pay 10 percent if the Liberals are elected (a 60 percent probability), zero otherwise. Either the Conservatives or the Liberals will be elected. a) Devise an investment strategy that guarantees at least a 4.4 percent return, no matter which party wins the election. b) Devise an investment strategy that is risk-free, that is, one in which the return on your $2000 does not depend at all on which party wins

**A** In order to get a 4.4% return, you want to earn $2000*0.044 = 88. Suppose you put $x to Lion, then you earn an expected value of (8%)(40%)x = 0.032x. If you put x into Lions, then that means 2000-x into donkey, and the expected earning is (2000-x)(10%)(60%) = 0.06(2000-x). To get $88, we solve 0.032x + 0.06(2000-x) = 88 for x. We can find x = 8000/7.

B. Suppose you put $x into Lions. Because either the liberals win or the conservatives win, so either you get 0.08x, or (2000-x)0.1. It doesn't matter what the probability is, as the bottom line is you will get one of the two things, so all you need is to equate them to ensure you earn that amount. 0.08x = (2000 - x)0.1 and solve for x.

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