The purpose of this problem is to study the sacrifice ratio. Suppose that initia

Question

The purpose of this problem is to study the sacrifice ratio. Suppose that initially actual and natural real GDP both equal 11,000 and that the rate of inflation is 3.5 percent. Natural real GDP grows by 3 percent per year over the next five years, but then grows by 4 percent in the second year, 5.5 percent in the third year, 4.2 percent in the fourth year, and 3.5 percent in the fifth year. Inflation in years 1-5 equals 3.1 percent, 2.2 percent, 1.6 percent, 1.3 percent, and 1.1 percent, respectively.
(a) Calculate natural real GDP for years 1-5.
(b) Calculate actual real GDP for years 1-5.
(c) Calculate the output ration for years 1-5.
(d) Calculate the cumulative loss of output for years 1-5.
(e) Calculate the sacrifice ratio.

Explanation / Answer

Part a)
Natural GDP at end of first year = 1.03 * 11000 = 11330
Natural GDP at end of second year = 1.03 * 11330 = 11669.9
Natural GDP at end of third year = 1.03 * 11669.9 = 12020
Natural GDP at end of fourth year = 1.03 * 12020= 12380.6
Natural GDP at end of fifth year = 1.03 * 12380.6= 12752
Cumulative sum = 60152.5

Part b)
Actual GDP at end of first year =0.98* 11000 = 10780
Actual GDP at end of second year = 1.04 * 10780 = 11211.2
Actual GDP at end of third year = 1.055 * 11211.2 = 11827.8
Actual GDP at end of fourth year = 1.043 * 11827.8= 12324.6
Actual GDP at end of fifth year = 1.035 * 12324.6 = 12756

Part c )
The output ratio = Real(Actual) GDP / Natural GDP
For first year = (10780/ 11330) * 100 = 95.1
For Second year = (11211.2 / 11669.9) *100 = 96.1
For third year = (11827.8 / 12020)*100 = 98.4
For fourth year = (12324.6/ 12380.6) *100 = 99.5
For fifth year = ( 12756/ 12752)*100 = 100

Part D)
loss of output for a year = 100 – output ratio
For year 1 loss = 100-95.1 = 4.9
Year 2 loss= 100 -96.1= 3.9
Year 3 loss= 100 – 98.1= 1.6
Year 4 loss= 100- 99.5 = 0.5
Year 5 loss = 100-100 = 0
Cumulative loss = 10.9

Part E )
Reduction in inflation rate = 3.5-1.1= 2.4
Hence sacrifice ratio = 10.9/2.4 = 4.5

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