Prices change over time and macroeconomic measures of total output that reflect

Question

Prices change over time and macroeconomic measures of total output that reflect a country's standards of living or productive capacity need to adjust for these price changes (i.e. inflation The U.S. Department of Commerce's Bureau of Economic Analysis (BEA) used to calculate real GDP (until 1996) through a "fixed-base-year" method. Instead of using the market value of a good (or service) at each point of time t, each good is priced at its market value in a base year. Suppose this base year is equal to tb. Then, real GDP at time t with base year tb is equal to: "You can e matotalof 100pcants. Pleasenotifymeabout any-typContact: chenyebaillinois.ed. a. For what year t does NGDP coincide with GDP? b. Real GDP at time t with base year tb can be expressed as GDP =1mtPrQe. Find a mathematical expression for . What is its economic interpretation? c. Derive the growth rate of GDPb. How does it relate to the growth rates of the prices and quantities of each individual good/service j? Argue why GDP is a more suitable measure than NGDP for comparing a country's living standards or productive capacity over time. d. Suppose there are only two goods j e (a b) and two periods of time t e fti,t2). Derive real GDP at both periods given a base year tb. Does the choice of the base year t affect the level of real GDP? Is this also the case for the growth rate of real GDP? e. Argue why GDPb is not necessarily a good measure for real GDP.

Explanation / Answer

a.For the base year nominal GDP (NGDP) and real GDP (GDP) will e equal. Thus the value of t will be 1 for NGDP to be equal to GDP.

b.Nominal gdp would be

NGDP = PjtQjt that is current prices multiplied by goods produced in the current year.

While real GDP would be

GDP = PjtbQjt that is base year prices multiplied by goods produced in the current year.

Now in the question it is given that Real GDP as

GDP = x PjtQjt -------------- A ( I am designating this as equation A)

( I am taking gamma sign as x as it is difficult to type gamma here)

So x basically is an expression of relation between nominal and real prices or base year prices.

Now let r be the rate of growth in prices and n be the number of years since base year.

So,

Current price = base price * (1+r/100)n

i.e.

Pjt = Pjtb *( 1+r/100)n .

Now, rearranging the above equation

Pjtb = Pjt / (1+r/100)n -------------------- B(I am designating this as equation B)

Now comparing equation A and B we get,

X= 1/( 1+r/100)n

c.Let the growth rate of goods and services in the economy be z% per annum and n be the number of years elapsed since base year.

Now, real GDP will depend upon growth rate of production of goods and services. Since we use base year prices only in calculation of real GDP, the real GDP growth will not depend on the rate of growth of prices of the goods and services.

Therefore mathematically growth rate of real GDP is basically the growth rate in productive capacity i.e. rate of growth of goods/services in the economy.

So, mathematical expression for growth rate of real GDP is simply z% per annum.

For a particular year

GDPn = GDPb (1+z/100)n

Where   GDPn = Real GDP of nth year

And GDPb = real GDP of base year.

Real GDP (GDP) is more suitable measure than nominal GDP(NGDP) for comparing a country’s living standards or productive capacity as shows growth only in productive capacity and not in their prices. In NGDP we see increase in prices too, so it may happen that NGDP will increase even when prices increase a lot and Quantity does not increase at all or has decreased. If quantity has decreased GDP will show a decrease, but NGDP may show even an increase due to increase in prices.

d. Let r1 and r2 be growth rates of goods a and b respectively and

Let p1 and p2 be the prices of a nd b respectively in the base year

Let Qa and Qb be the Quantities of goods a and b produced in the base year.

Now,

GDPb = p1.Qa.p2.Qb

GDPt1 = p1.Qa(1+r1/100)t1 *p2.Qb(1+r2/100)t1

Similarly,

GDPt2 = p1.Qa(1+r1/100)t2 *p2.Qb(1+r2/100)t2

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