Question

2. Effect of Investment Suppose in a closed private economy households are spending 75 cents from each additional dollar that they receive as an income. Moreover, when they do not have any income, they are still spending $100 on their needs. (a) Derive the consumption function and the saving function in this economy. Draw the graphs in the (C-Y) space and in the (S-Y) space. (b) If there is no investment in the economy, what is the equilibrium level of output? (c) Suppose autonomous investment of $60 is added. What are the two ways to calculate the new equilibrium level of output? Is the change in equilibrium level of output the same as the change in autonomous expenditures? How can you explain the result? Give the intuition. Redraw the graphs from point (a) and show the changes on both graphs. (d) Suppose that output is (i) $600 and (ii) 700. In each case what is the amount of the planned expenditures and of the actual expenditures? of planned investment and of saving? What would happen to the level of output in each case? Explain why. Compare the amount of unintended inventory investment with the change in output. How can you explain the difference? Redraw the resulting graphs from point (c) and show both situations on your both graphs.

Answer 1

A) C =a +mpc*y ,where C is consumption, a is autonomous consumption ( C at Y=0), mpc is Marginal propensity to consume and y is income.

C=100+0.75y. { Consumption function}

S=-a+(1-mpc)*Y. , S is saving

S=-100+(1-0.75)y=-100.25Y

B) equilibrium income,

Y=C+I

I=0

Y=C

Y=100+0.75Y

0.25Y=100

Y=100/0.25=400

C) first way,

Y=C+I

I=60

Y=100+0.75y+60

Y=160+0.75Y

Y=160/0.25=640

Second way,

Equilibrium y at where Saving equal to investment

S=I

-100+0.25Y=60

0.25y=160

Y=160/0.25=640

∆in autonomous expenditure=60

∆ y=640-400=240

No ,the change in income is more than change in autonomous spending.

The income is Increase more than autonomous spending Increase is because of Multiplier effect of autonomous spending.as autonomous expenditure Increases ,that expenditure becomes someone else income ,so he also spend on more goods and this expenditure also becomes someone else income and he also spend increased income on goods and this process keep going on and new income keep generate until next Increase in income is zero. So that why change in income is more than change in autonomous spending change.

D) i) y=600{ planned expenditure}

Actual expenditure=100+0.75*600+60=100+450+60=610

Planned investment=60{ fixed}

Saving=-100+0.25*600=-100+150=50

As actual expenditure is higher than planned expenditure,Stocks of inventories start to fall, so firms hire new workers and increase production.

Unintended inventory investment=600-610=-10

ii) y=700{ planned expenditure}

Actual expenditure=100+0.75*700+60=100+525+60=685

Planned investment=60

Saving=-100+0.25*700=-100+175=75

As actual expenditure is lower than planned expenditure,Firms start to acquire excessive inventories and so they lay off workers and reduce production until their inventories are stable again.

Unintended inventory investment=700-685=15