Question

Assume that in the first quarter of 2020, real GDP and potential GDP were both $20 trillion and the unemployment rate was 3.5%. Assume that potential GDP is still $20 trillion in the second of 2020 but that actual real GDP is $19 trillion.

a. What is the annualized growth rate of real GDP between the first and second quarters?

b. What is the output gap in the second quarter of 2020?

c.   According to Okun’s law, what will be the unemployment rate in the second quarter of 2020?

d. Assume that in the second quarter consumption is equal $13 trillion, net exports are equal to -$0.5 trillion, and government purchases and planned investment are both equal to $3 trillion. What is the amount of inventory investment?

Answer 1

In the first quarter of 2020, real GDP and potential GDP were both $20 trillion and the unemployment rate was 3.5%.

Hence, natural rate of unemployment is

u* = 3.5%

Now, in the second quarter of 2020, potential GDP is still $20 trillion, but that actual real GDP is $19 trillion.

(a) Hence, in the first quarter of 2020, Real GDP is

Y1 = $20 trillion

And, in the second quarter of 2020, Real GDP is

Y2 = $19 trillion

Hence, change in Real GDP is

(Y2 - Y1) = $19 trillion - $20 trillion

or, (Y2 - Y1) = -$1 trillion

Hence, the annualized growth rate (g) of real GDP between the first and second quarters is

g = (Y2 - Y1)/Y1

or, g = -1/20

or, g = -0.05 or -5%

Hence, the annualized growth rate of real GDP between the first and second quarters is (-5%).

(b) The output gap in the second quarter of 2020 is

= (Y2 - Y1)

= -$1 trillion

This is a recessionary gap.

Hence, the output gap in the second quarter of 2020 is:

Recessionary gap of $1 trillion.

(c) According to okun's law,

(Y - Y*)/Y* = 2.(u - u*)

Where, Y = Real GDP, Y* = Potential GDP, u = Unemployment Rate and u* = Natural Unemployment Rate.

Here, Y* = $20 trillion, Y = $19 trillion, u* = 3.5%.

Hence, using Okun's Law we get,

(19 - 20)/20 = 2×(u - 3.5)

or, 2.u = 6.95

or, u = 3.475%

The Unemployment rate at the second quarter of 2020 will be 3.475%.

(d) In the second quarter,

Consumption is

C = $13 trillion

Net Exports is

NX = -$0.5 trillion

Government Purchases is

G = $3 trillion

Hence, Aggrigate Expenditure is

AE = C + G + NX

or, AE = 13 + 3 - 0.5

or, AE = $15.5 trillion

And, Actual Real GDP in the second quarter of 2020 is

Y = $19 trillion

Hence, The amount of Inventory Investment (I) is

= (Y - AE)

= $19 trillion - $15.5 trillion

= $3.5 trillion

The amount of inventory investment is $3.5 trillion.

Hope the solutions are clear to you my friend.