Question

Suppose the economy is characterized by the following behavioral equations:

C=c0 +c1YD YD = Y – T I=b0 +b1 Y

Government spending and taxes are constant. Note that investment now increases with output.

1. (1) Solve for equilibrium output.

2. (2) What is the value of the multiplier? How does the relation between investment and output affect the

   value of the multiplier? For the multiplier to be positive, what condition must (c1 + b1) satisfy?

3. (3) Suppose that the parameter b0, sometimes called business confidence, increases. How will equilibrium output be affected? Will investment change by more or less than the change in b0? Why?

   What will happen to national saving?

Answer 1

ans1)

Here,

c0 is autonomous consumption

c1 is marginal propensity to consume(mpc)

YD is disposable income

b0 autonomous investment

b1 marginal propensity to invest.

Y=C+I

=> Y-T=c0+c1YD+b0+b1Y

=> Y-b1Y-T= c0+c1(Y-T)

=>Y-b1Y-T= c0+c1Y-c1T

=>Y-b1Y-c1Y=c0-c1T+T

=>Y(-b1-c1)= c0 -T(c1-1)

=>Y={ c0-T(c1-1)}/(-b1-c1)

ans2) Multiplier is an economic factor, when increased or changed, causes increases or changes in many other related economic variables. It is an propotional amount of increase or decrease.

The multiplier depends on your mpc or mps

so, multiplier is 1/(1-mpc)

= 1/(1-c1)

The more the investment the more income will be generated and yet again a high mpc which will boost the economy.

Since mpc is less than 1, then 1/(1-mpc) will be greater than 1. Higher the mpc higher is the multiplier.

ans 3) when b0 increases then it will increase the income . It induces economic growth. When income increases due to investment then these increments are used to purchase goods, the output of consumer goods are increased to meet thid demand caused by increase in income. The income will change more than b0 due to its multiplier effect. According to keynes, it will lead to paradox of thrift. The attempt by all to save more will decline the equillibrium level of income .