a Starting with a supply side growth rate of 3 assume that d

a) Starting with a supply side growth rate of 3%, assume that due to the severity of the recession, annual supply side growth rate decreases to 2% beginning in 2009q1. Potential GDP will be the same as with the 3% calculation through 2008q4 and then grow at a slower 2% rate after that. Calculate the value of potential GDP that could have been realized in 2015q3 using the 2% supply side growth rate starting in 2009q1. Remember that 3% and 2% are annual growth numbers and we are dealing with quarterly observations when you make the calculation for 2015.

b) What is the amount of the output gap?

Solution

(a) Potential GDP in 2009_q1 = $14,375 billion

Growth rate = 2% or 0.02

Calculate Potential GDP in 2010_q1 -

Potential GDP = Potential GDP in 2009_q1 * (1+r)ⁿ = $14,375 billion * (1+0.02)¹ = $14,662.5 billion

Calculate Potential GDP in 2011_q1 -

Potential GDP = Potential GDP in 2010_q1 * (1+r)ⁿ = $14,662.5 billion * (1+0.02)¹ = $14,955.7 billion

Calculate Potential GDP in 2012_q1 -

Potential GDP = Potential GDP in 2011_q1 * (1+r)ⁿ = $14,955.7 billion * (1+0.02)¹ = $15,254.8 billion

Calculate Potential GDP in 2013_q1 -

Potential GDP = Potential GDP in 2012_q1 * (1+r)ⁿ = $15,254.8 billion * (1+0.02)¹ = $15,559.9 billion

Calculate Potential GDP in 2014_q1 -

Potential GDP = Potential GDP in 2013_q1 * (1+r)ⁿ = $15,559.9 billion * (1+0.02)¹ = $15,871.1 billion

Calculate Potential GDP in 2015_q1 -

Potential GDP = Potential GDP in 2014_q1 * (1+r)ⁿ = $15,871.1 billion * (1+0.02)¹ = $16,188.5 billion

Calculate Potential GDP in 2015_q2 -

AS we have to now calculate the GDP for one quarter only, rate of growth will be divided by 4 and time period will be multiplied by 4.

There are 4 quarters in the year.

Potential GDP = Potential GDP in 2015_q1 * (1+r)ⁿ = $16,188.5 billion * (1+0.005)⁴ = $16,512.3 billion

Calculate Potential GDP in 2015_q3 -

Potential GDP = Potential GDP in 2015_q2 * (1+r)ⁿ = $16,512.3 billion * (1+0.005)⁴ = $16,842.5 billion

The value of potential GDP in 2015_q3 is $16,842.5 billion.

(b) Calculate Output gap -

Output gap = Actual real GDP - Potential GDP

                 = $16,414.0 billion - $16,842.5 billion

                 = -$428.5 billion

The amount of output gap is -$428.5 billion.