Slides for Part III-B These slides will take you through the basics of income- expenditure analysis. The following is based on Dornbusch & Fisher, Chapter 3 (on reserve)

The Keynesian system is based on the principle of aggregate demand, which can be stated as follows: in the short period (that is, the time period in which productive capacity is fixed within narrow limits), real output and employment are determined by aggregate demand. Aggregate demand (AD) is defined as total or aggregate spending for newly produced goods and services. Introduction to the Keynesian system

AD = C + I + G + NX Components of Aggregate Demand (AD) For an open economy with government C, I, and G mean the same thing as always; NX is net exports

Equilibrium with constant AD Output Aggregate demand AD = Y AD 6 6 IU > 0 IU < 0 E IU is unplanned inventory investment

Properties of equilibrium Planned spending is equal to real output, meaning the plans of spending and producing units match up. Unplanned inventory investment is equal to zero. Firms on average have no reason to expand or contract the scale of production. Nor do they have a reason to offer more or less employment.

$8 trillion is a disequilibrium value of real output Output (trillions) Aggregate demand AD = Y AD 6 6 IU = $2 trillion IU < 0 E IU = Y - AD 8

Let: Y is real output or real GDP. YD is real disposable income.  For a closed economy without a public sector, the following must be true: AD = Y = YD [1] “My spending is your income.”  In a closed economy with no public sector: AD = C + I [2]  Thus, developing a theory of aggregate demand logically begins with a theory of consumption and a theory of investment.

The consumption function The consumption function is given by: 0 < c < 0 C is the intercept of the consumption function, or the component of planned household spending determined independent of income. c is the marginal propensity to consume-the change in consumption resulting from a one unit change in disposable income.

Y S S = Y The saving function The slope of the saving function is given by MPS

The consumption function and aggregate demand Income, Output Aggregate demand AD = Y AD 0 E Y0Y0

a R.F. Kahn. “The Relation of Home Investment to Unemployment,” Economic Journal, June  Kahn’s Problem a : What would be the limit of new employment created if the government undertook to stimulate employment growth by spending for public works projects? þ Expenditure for public works þ Increase in employment in construction trades and building supplies industries þ Increase in income of people employed in these industries þ Increase in spending for consumption goods increase in employment in consumption goods industries. The multiplier effect

Let Y = C + I C = YD I = 300 Thus we have: Now, allow for a $100 increase in autonomous investment, that is:

AD 1 AD 2 AD =Y Aggregate demand Y Y0Y0 II Output, Income 45 0

Deriving the multiplier Let Y  C + I (1) Therefore:  Y =  C +  I (2) where (3) (4) Let (5) Thus: Rearrange (5) (6)

Rearrange (6) Example:

RoundIncrease in demand this round Increase in production this round Total increase in income The multiplier

Be advised that the multiplier effect works in both directions

The government sector Let YD denote disposable income; TR is transfer payments; TA is taxes Thus, we can say: YD = Y + TR – TA Also: (4a, p. 69)

Specification of fiscal policy Fiscal policy is public policy with respect of government spending, transfer spending, and the structure of taxes or revenue collection We assume that: where t is the marginal propensity to tax out of national income (Y), that is t =  TA/  Y, where 0 < t < 1

The closed model with government Substitute (5) and (6) into (2) to obtain (7) (1) (2) (3) (4) (5) (6) (7)

Substitute (7), (3) and (4) into (1) to obtain (8) Rearrange (8) to obtain (9) Let: (8) (9)

To find equilibrium Y (Y 0 ): Now rewrite (9) as follows: Rearrange (10) to obtain (11): (10) (11)

Use the following set-up to answer the questions on the next slide Y = C + I + G C = YD I = 110 G = 180 TR = 240 TA =.2Y

1.What is the value of the tax multiplier? 2.Solve for equilibrium output (Y 0 ) and illustrate with an income expenditure diagram. 3.Calculate disposable income (YD) when Y = Y 0. 4.Calculate saving (S) when Y = Y 0 5.Calculate the change in output (  Y 0 ) resulting from a $20 decrease in investment. 6.Assuming the equilibrium value of income is equal to that which you computed in (2) above, what is the value of unplanned inventory investment if actual output is equal to $1400?