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If you could design an ideal experiment to answer this question, how would you do so? Do you think it would be pract

Suppose that you are interested in answering the question of how consumption reacts to tax cuts. In recent years, recessions have been countered with tax rebates, wherein households are sent a check for several hundred dollars. This check amounts to a “rebate” of past taxes paid. If you could design an ideal experiment to answer this question, how would you do so? Do you think it would be practical to use this experiment on a large scale?

Why do you think this simple correlation might give a misleading sense of the eﬀect of changes in the interest rate on GDP? How might a model help you answer this question?

During recessions, central banks tend to cut interest rates. You are interested in understanding the question of how interest rates aﬀect GDP. You look in the data and see that interest rates tend to be low when GDP is low (i.e. the interest rate is procylical). Why do you think this simple correlation might give a misleading sense of the eﬀect of changes in the interest rate on GDP? How might a model help you answer this question?

Which of these failures is problematic for your model and which is not? Why?

Suppose that you want to write down a model to explain the observed relationship between interest rates and aggregate economic spending. Suppose that you want to test other predictions of your model. You consider two such predictions. First, your model predicts that there is no relationship between interest rates and temperature, but in the data there is a mild negative relationship. Second, your model predicts that consumption and income are negatively correlated, whereas they are positively correlated in the data. Which of these failures is problematic for your model and which is not? Why?

Using the constraint, solve for x as a function of y and ¯ u. Substitute your solution into the objective function. Now you are choosing only one variable, y, to minimize expenditure.

This question demonstrates why the CPI may be a misleading measure of inﬂation. Go back to Micro Theory. A consumer chooses two goods x and y to minimize expenditure subject to achieving some target level of utility, ¯ u. Formally, the consumer’s problem is
min x,y
E=pxx+pyy s.t. ¯ u=xαyβ Total expenditure equals the price of good x times the number of units of x purchased plus the price of good y times the number of units of y purchased. α and β are parameters between 0 and 1. px and py are the dollar prices of the two goods. All the math required for this problem is contained in Appendix A.
(a) Using the constraint, solve for x as a function of y and ¯ u. Substitute your solution into the objective function. Now you are choosing only one variable, y, to minimize expenditure.
(b) Take the ﬁrst order necessary condition for y.
(c) Show that the second-order condition is satisﬁed. Note, this is a one variable problem. (d) Use your answer from part b to solve for the optimal quantity of y, y∗. y∗should be a function of the parameters α and β and the exogenous variables, px,py and ¯ u. Next, use this answer for y∗ and your answer from part a to solve for the optimal level of x, x∗. Note, the solutions of endogenous variables, x∗and y∗in this case, only depend on parameters and exogenous variables, not endogenous variables. (e) Assume α=β=0.5 and ¯ u=5. In the year 2000, px=py=$10. Calculate x ∗ 2000,y∗2000 and total expenditure, E2000. We will use these quantities as our “consumption basket” and the year 2000 as our base year. (f) In 2001, suppose py increases to $20. Using the consumption basket from part e, calculate the cost of the consumption basket in 2001. What is the inﬂation rate?
(g) Now use your results from part d to calculate the 2001 optimal quantities x∗2001 and y∗2001 and total expenditures, E2001. Calculate the percent change between expenditures in 2000 and 2001.
(h) Why is the percent change in expenditures less than the percent change in the CPI? Use this to explain why the CPI may be a misleading measure of the cost of living.

Calculate GDP using the production and income methods.

Suppose an economy produces steel, wheat, and oil. The steel industry produces $100,000 in revenue, spends $4,000 on oil, $10,000 on wheat, pays workers $80,000. The wheat industry produces $150,000 in revenue, spends $20,000 on oil, $10,000 on steel, and pays workers $90,000. The oil industry produces $200,000 in revenue, spends $40,000 on wheat, $30,000 on steel, and pays workers $100,000. There is no government. There are neither exports nor imports, and none of the industries accumulate or deaccumulate inventories. Calculate GDP using the production and income methods.

Suppose the unemployment rate is 6%, the total working-age population is 120 million, and the number of unemployed is 3.5 million. Determine:

(a) The participation rate.
(b) The size of the labor force.
(c) The number of employed workers.
(d) The Employment-Population rate.

What is the incremental wealth associated with your decision

Tasty Pies is expanding its business and wants to open a new facility to make frozen pies, which requires a new automated pie maker. One such pie maker can be purchased for $300,000. Alternatively, it can be leased for $52,000 per year for seven years and lease rentals need to be paid annually in advance. The management informs you that the new pie maker can be fully depreciated to zero using the straight-line method over four years and that its scrap/residual value is expected to be $5,000 at the end of the lease. Tasty Pies has estimated that the appropriate after-tax opportunity cost of capital of the expansion is 19% per annum, and the net present value of the expansion is expected to $10,000.
Tasty Pies pays tax at the rate of 30% and it can borrow funds at a before-tax rate of 11% per annum. All cash-flows have been quoted on a before-tax basis. Would you recommend that Tasty Pies buy or lease the pie maker? What is the incremental wealth associated with your decision

In a DCF set-up, the analyst can easily modify input variables such as growth (from year to year), reduction in costs, increase in operational efficiency (margins) etc. and compute the change in value of the target in the future.

In a DCF set-up, the analyst can easily modify input variables such as growth (from year to year), reduction in costs, increase in operational efficiency (margins) etc. and compute the change in value of the target in the future.

Briefly explain why the discounted cash flow (DCF) method allows the analyst to directly assess the effects of operational improvements and other synergistic efficiencies.

An economy produces three goods: houses, guns, and apples. The price of each is $1. For the purposes of this problem, assume that all exchange involving houses involves newly constructed houses.

(a) Households buy 10 houses and 90 apples, eating them. The government buys 10 guns. There is no other economic activity. What are the values of the diﬀerent components of GDP (consumption, investment, government spending, exports/imports)?
(b) The next year, households buy 10 houses and 90 apples. The government buys 10 guns. Farmers take the seeds from 10 more apples and plant them. Households then sell 10 apples to France for $1 each and buy 10 bananas from Canada for $2 each, eating them too. What are the values of the components of GDP?
(c) Return to the economy in part 1a. The government notices that the two richest households consume 40 apples each, while the ten poorest consume one each. It levies a tax of 30 apples on each of the rich households and gives 6 apples each to the 10 poorest households. All other purchases by households and the government are the same as in (a). Calculate the components of GDP