# Consider a one-period closed economy, i.e. the consumer lives for one period. He/She supplies… 1 answer below »

Assignment 1

E322 Intermediate Macroeconomics

Siming Liu

(100 points in total)

Due by February 1, in class.

1 Static consumption-labor choice (30 points)

Consider a one-period closed economy, i.e. the consumer lives for one period. He/She supplies

labor, earns wage incomes and demands consumption goods. The government needs to finance an

exogenous spending via distorting labor tax. That is to say, for each dollar of wage income the

consumer earns, he/she needs to pay t fraction to the government. t here indicates the tax rate: a

policy variable. In addition to the wage income, the consumers are also shareholders of the firms.

So, he/she gets constant dividend payment before making decision.

1.1 Solve the consumer’s consumption-labor choice problem, taking prices and government policies

as given (partial equilibrium). More specifically, consider the following optimization problem:

max

c,l {c?(1 – l)1-?} (1)

s.t. c = w(1 – t )l + e (2)

where c is the consumption and l denotes the labor service supplied. e is the dividend payment

from the firms.

(Note: By solving the problem, I mean you should get all equilibrium allocations as functions of

parameters: c*(w, t, ?), l*(w, t, ?).)

1.2 Suppose the government needs to increase the tax rate to finance a higher level of government

spending. Think about how that affects the equilibrium labor supply l*.

1.2.1: If e > 0, what will happen?

1.2.2: If e = 0, what will happen?

1.2.3: If e

1.2.4: Analyze the effects of this tax rate change on consumption/labor choice using appropriate

1.3. Based on the above solutions of private equilibrium, write out the government’s tax revenue

as a function of tax rate, taking the wage rate as constant. Define tax revenue = twl*(t ). Is

the tax revenue always increasing in t? (Laffer curve)

2 Three ways to calculate GDP (20 points)

Consider an economy with two firms. Firm A produces orange and Firm B produces orange juice.

In a given year, Firm A produces 10 million pounds oranges, sells 4 million pounds of these

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oranges to Firm B, sells 3 million pounds oranges to domestic consumers, and exports 3 million

pounds oranges. Each pound of orange is sold at \$1. Firm A pays \$6 million in wages to domestic

workers and \$1 million tax to the government. Firm B produces 4 million boxes of orange juice.

In addition, they import 2 million boxes of orange juice. The import price of orange juice is \$2

per box. 5 million boxes of orange juice are sold to domestic consumers at \$3 per box, and the

remaining 1 million boxes of orange juice is stored in the inventory. Firm B pays \$5 million in

wages to the domestic workers, and pays \$2 million in taxes to the government. The government

provides education for the domestic consumers, and the cost of the educational services is just the

wages paid to the teachers, which is \$4 million. Finish the following tasks and briefly show the steps.

2.1 Calculate the GDP using product approach.

2.2 Calculate the GDP using expenditure approach.

2.3 Calculate the GDP using income approach.

3 Nominal and real GDP (15 points)

Consider an economy with two goods produces, computers and bicycles. The following Table summarizes

the production and price information of these two goods over two years:

Price Quantity

Year 1

computers \$ 500 10

bicycles \$ 50 100

Year 2

computers \$ 600 20

bicycles \$ 80 120

3.1 Compute the Nominal GDP in both years. What is the rate of growth of nominal GDP?

3.2 Compute the Real GDP in both years using Year 1 as the base year. What is the rate of

growth for real GDP?

3.3 Compute the implicit GDP price deflator, and the inflation from year 1 to year 2.

3.4 Suppose that computers in year 2 are of higher quality compared to computers in year 1.

How would such information bias your results? Explain.

4 Saving-investment equation (15 points)

Consider an economy with total GDP of \$15 trillion, total household consumption of \$10 trillion,

total government spending of \$3 trillion, imports of \$4 trillion and exports of \$3 trillion. The net

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factor payments households receive is \$0.2 trillion, and the total taxes paid to the government are

\$2 trillion.

4.1 Calculate the total private investment in this economy.

4.2 Calculate gross national product.

4.3 Calculate the total national saving.

4.4 Calculate the current account surplus.

5 Data question (20 points)

Follow the following steps to organize the data you will need to do this question.

(a) Go to website of Federal Reserve Bank of St. Louis (FRED Economic Data):

quarterly and nominal variables. There are versions of the variables which are

not seasonally adjusted, with different frequency (monthly, annual), and which are in

nominal versions of the variables. All the variables names and codes are reported below.

(b) The variables might have different starting points. Pick the latest starting point as your

initial point for all variables.

• Personal Consumption Expenditures: Durable Goods (variable name: PCDG)

• Personal Consumption Expenditures: Services (variable name: PCESV)

• Personal Consumption Expenditures: Nondurable Goods (variable name: PCND)

(e) Click on Price Indexes & Deflators. Download Gross Domestic Product: Implicit Price

Deflator (variable name: GDPDEF)

5.2 Using the GDP implicit price deflator, convert all the above nominal variables into real

variables. Basically, you have to divide each variable with the price deflator and multiple it

with 100.

5.3 Apply HP-filter for each variable. You can use the HP-filter provided in the following website:

http://dge.repec.org/cgi-bin/hpfilter.cgi. Use default penalty parameter (1600). For the

second question choose “log”, and for the third question choose “deviations from trend”.

For the last question, it depends on how you save the data. Most likely, your data points

are separated by new lines, so choose “new line” if that is the case. If your data points are

separated otherwise, choose the corresponding option from the list.

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5.4 Plot detrended GDP and detrended consumption of durables together.

5.5 Plot detrended GDP and detrended consumption of nondurables together.

5.6 Plot detrended GDP and detrended consumption of services together.

5.7 What differences do you notice in these graphs regarding the correlation, lead-lag relation,

and volatility comparisons of these variables?

5.8 Provide an explanation for the differences you observe in the [5.7] part.

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