National Income Determination Two-Sector National Income Model Lecture 2 National Income Determination Two-Sector National Income Model

Outline Equilibrium Conditions: Output-Expenditure Approach Graphical approach Algebraic approach Saving Function Equilibrium Conditions: Injection-Withdrawal Approach Changes in income Expenditure Multiplier Paradox of Thrift

Recap 2-sector model to explain the size of the national income and what causes changes to it Planned expenditure is composed of Consumption and Investment Functions and graphical illustrations National Income identities Y  E C + S  C + I  S  I Changes in these components of expenditure lead to changes in national income (autonomous changes) Changes in national income can cause changes in expenditure, and national income (induced change)

Output-Expenditure Approach National income is in equilibrium when actual output = planned expenditure We have planned expenditure, E equal to C+I Equilibrium income is Ye=planned E A 45°-line is the locus of all possible points where Y = E Above the line, E>Y Below the line, E<Y Graphical Illustration

Output-Expenditure Approach: A Graphical Illustration Y = E Planned E < Y C, I, E AE Y= E Planned E > Y Y Ye

Output-Expenditure Approach: More Generally Y = planned E Y = I* + cY Y = I*+ cY (1-c)Y = I* Equilibrium condition Y* = I* x 1 1-c

Output-Expenditure Approach: Algebraic Solution Let the level of Investment, I= 100 MPC= 0.8, implying that C= 0.8Y Aggregate expenditure, E = C + I E= 0.8Y + 100 In equilibrium, E= Y Y= 0.8Y + 100 0.2Y= 100 Y= 500

Savings Functional form We have Y  C + S Saving function can simply be derived from the consumption function S = Y – C if C = cY S = Y – cY S = (1-c) Y S = sY (recall that s = 1 – c)

Saving Function S S = sY S = (1-c)Y Slope of tangent = s =1- c Y

Saving Function Marginal Propensity to Save MPS = s It is defined as the change in saving per unit change in disposable income MPS = S/ Y It is the slope of tangent of the saving function

Saving Function Average Propensity to Save APS It is defined as the total saving divided by total income APS = S/Y

Saving Function Average Propensity to Save APS (cont’d) When S= sY  APS = MPS = s = constant

Withdrawals-injections method: Algebraic approach Equilibrium conditions under the withdrawals-injection approach Graphical approach

Withdrawals-injections method: Algebraic approach Y= C+ S And… E= C + I In equilibrium, Y= E Implying that C+ S= C + I Indicating that S= I Let I= I* and S= sY If S= I at equilibrium, then sY= I* Y= I*(1/s) …compare with O/E method

Equilibrium Income No matter which approach you use (i.e. output/ expenditure or withdrawals/injections), you will get the same equilibrium condition.

What Forces Cause Income, Y, to Change in the 2-sector Economy? Movements along the curve vs. Shifts of the curve A movement along a curve represents a change in expenditure in response to a change in income A shift of a curve represents a different level of expenditure associated with each level of income

Graphical Illustrations- Movements along the Curve: I,C,S functions/ expenditure flows Income is initially at Y0 and rises to Y1. Investment remains constant Consumption increases from C0 to C1 Savings increases from S0 to S1 The slope of each expenditure line is a measure of the responsiveness of the flow to a change in income The slope is called a marginal propensity eg. MPC, MPS

Graphical Illustrations- Shifts of the expenditure flows The curves themselves could shift, with no change in income At each level of income, Y0, more is invested, consumed and less is saved

Shifts in Expenditure Functions How does national income change when expenditure flows change? Only two things in this model that can bring about a change in expenditure flows Consumption Investment

A shift in the Investment Function Investments are an injection and have expansionary effects on economy Illustrations using the output- expenditure and injection- withdrawals approaches

A shift in the Consumption Function Assume that there is a rise in the proportion of income that people wish to spend (and a corresponding fall in savings) Illustrations using the output- expenditure and injection- withdrawals approaches