Answer to Question #243358 in Macroeconomics for Raymond

Question

Suppose that permanent income is calculated as the average of income over the past five years; that is,

YP = 1/5( Y + Y-1 + Y-2 + Y-3 + Y-4 ) (P1)


Suppose further that consumption is given by C = .9 YP .


a. If you have earned $20,000 per year for the past 10 years, what is your permanent income?


b. Suppose that next year (period t + 1) you earn $30,000. What is your new YP ?


c. What is your consumption this year and next year?


d. What is your short-run marginal propensity to consume? Long-run MPC ?


e. Assuming you continue to earn $30,000 starting in period t + 1, graph the value of your permanent income in each period, using equation (P1).

Answer 1

The permanent income can be calculated as the average income over the as shown below;

$YP=1/5(Y_t+Y_{t-1}+Y_{t-2}+Y_{t-3}+Y_{t-4})$

Consumption is given by $C=0.9YP$

a) If the income for the last 10 years is the same at $20000

$YP=1/5(20000+20000+20000+20000+20000)=\$20000$

b) If the income for the next period raised to $30000 in period (t+1) the permanent

$YP=1/5(Y_t+Y_{t-1}+Y_{t-2}+Y_{t-3})=1/5(30000+20000+20000+20000+20000)=\$22000$

c) Consumption is given by $C=0.9YP$

consumption for this year can be calculated as shown

$C=0.9\times 20000=\$18000$

Consumption for the next year can be calculated as shown below

$C=0.9\times 22000=\$19800$

d) The short run MPC is calculated as shown below

$MPC=1000/2000\times 1/5=0.18$

The long run MPC, C = $0.9YP$

$MPC=dC/dYP=0.9$

e) From the period (t+1) the income has increased to $30000 for all periods. The permanent income will keep on increasing for the next five years.

$YP_1=1/5(Y_{t+1}+Y_{t}+Y_{t-1}+Y_{t-2}+Y_{t-3})=1/5(30000+20000+20000+20000+20000)=\$22000$

$YP_2=1/5(Y_{t+2}+Y_{t+1}+Y_{t}+Y_{t-1}+Y_{t-2})=1/5(30000+30000+20000+20000+20000)=\$24000$

$YP_3=1/5(Y_{t+3}+Y_{t+2}+Y_{t+1}+Y_t+Y_{t-1})=1/5(30000+30000+30000+20000+20000)=\$26000$

$YP_4=1/5(Y_{t+4}+Y_{t+3}+Y_{t+2}+Y_{t+1}+Y_{t})=1/5(30000+30000+30000+30000+20000)=\$28000$

$YP_5=1/5(Y_{t+5}+Y_{t+4}+Y_{t+3}+Y_{t+2}+Y_{t+1})=1/5(30000+30000+30000+30000+30000)=\$30000$

The diagram showing the change in permanent income as average of last 5 years is changing for each period is given below: