Homework #1: Intermediate Macroeconomic Theory – Fall 2020

Question 1 

Consider an economy with two firms and a government. Firm 1 produces 10000 units of good X, which it sells for $20 per unit. It uses this revenue to pay $140000 in wages, $10000 in taxes, and $10000 in interest on a loan, with the rest as profits. Firm 1 sells some of its output to consumers, and some to Firm 2 as an intermediate good in their production process.

Firm 2 uses good X as an input into its manufacturing process. It buys 8000 units of good X and uses them to create 1000 units of good Y, which it sells for $400 per unit. It pays $200000 in wages and $20000 in taxes, with the rest as profits.

The government takes in taxes from only these two firms, and uses it to pay wages to provide government services, for instance national defense.

Please calculate GDP using the three different methods. (Of course, you’ll arrive at the same answer; however, indicate clearly what values you’re using in each case to arrive at the final answer, so as to illustrate you know what is included in each method of calculating GDP.)

1)Income approach:


2)Expenditure approach:


3)Product(value-added) approach:

Question 2 

Use the following price and quantity data for this question. For chain-weight with price average, use the method discussed in class.

Year 1

 QuantityPrice
X105
Y2010

Year 2

 QuantityPrice
X1510
Y4015

a)

Fill in the following chart:

YearNominal GDPreal GDP
(base=year 1)
real GDP
(base=year2)
real GDP
(chain-weight with price average)
Year 1    
Year 2    

b)

Fill in the follow chart, which asks you to calculate the inflation rate between years 1 and 2 using the Implicit GDP Price Deflator in three ways: year 1 as base year, year 2 as base year, and chain-weighting using price average.

 Inflation rate (%)
Base = Year 1 
Base = Year 2 
Chain-weighted, price average 

Question 3

Suppose that a representative consumer has the following utility function for leisure l and consumption C.    

                                         U(L, C) = C3/4 l1/4  

The real wage rate, w, is competitively determined to be 10. The number of hours, h, available to the consumer is 24. The profits, π, distributed to each consumer are 200 and taxes, T, are lump sum at 100.

a). Given the above, how much leisure and consumption would the consumer choose? 

b)Given the above, how many units of time will the consumer spend working?

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