MTopic 1 - The IS Curve

# MTopic 1 - The IS Curve - Topic 1 The I-S Curve...

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Topic 1 – The I-S Curve Introduction The I-S curve sets out all the possible combinations of real income (y) and the interest rate ( r ) consistent with equilibrium in the goods market A change in the rate of interest, r, affects equilibrium national income via the following route:- Where r is the change in the interest rate, I is the change in Investment and y is the change in real national income/output. Consider each of these 2 steps in turn STEP 1 – Investment and the Rate of Interest Investment is the purchase of capital goods ( i.e. plant, machinery, land, buildings etc. .). Investment is flow of expenditure per period (e.g. per quarter or per annum). If the volume of investment in a period is greater than the erosion of the capital stock due to wear and tear (depreciation ), the capital stock will be increasing. Typically, firms borrow to finance investment. At high rates of interest, the cost of borrowed money will be high and few investment projects will be viable. As interest rates fall, more and more investment projects become profitable. 1 r I y Via the multiplier

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Therefore there is a negative relationship between r and I as set out in Figure 1 Note that as interest rates fall from r 0 to r 1 , investment rises from I 0 to I 1 To sum up Step1:- r leads to I such that an increase in r reduces investment expenditures and a fall in r increases investment expenditures. Step 2:- Investment and Equilibrium Income Consider a simple model of national income determination for a closed economy with a government sector. Equation 1:- Aggregate Demand AD = C + I + G Where AD is Aggregate Demand, C is Consumers Expenditure or Consumption I is the level of Investment and G is the level of Government Expenditure 2 I r I= I(r) r 0 I 0 r 1 I 1 Figure 1 - The Investment Schedule
Equation 2 :- The Consumption Function C = a 0 + by D Where a 0 is autonomous consumption b is the marginal propensity to consume and y D is disposable or after tax income Note y D = y – ty where t is the income tax rate = (1-t)y Therefore C = a 0 + b (1-t) y The Consumption Function is set out in Figure 2 Equation 3:- The Investment Schedule I = I(r ) as set out above. N.B. we will assume a linear or straight line investment schedule. 3 y C C= a 0 +b(1-t)y a 0 Slope of function is b(1-t) Figure 2 - Consumption Function

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Equation 4:- Government Spending G = G 0 i.e. government spending is exogenous – it is the level decided upon by the Government. Equation 5 :- Equilibrium Condition AD = y [ aggregate demand is equal to output] Finding The Reduced Form The above model contains 5 equations. We will simplify matters by finding an expression for y in terms of The structural parameters (i.e b and t) The exogenous or autonomous variables (i.e. a 0 , I(r ), and G 0 ) This process is termed computing the reduced form and involves substituting Equations 2, 3 and 4 into Equation 1 and re-arranging Thus AD = y = C + I + G y= a 0 + [b(1-t)y] + I(r ) + G 0 Note that we have ‘y’ on both sides of this expression. Re-arranging
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## This note was uploaded on 05/05/2010 for the course COM 4123 taught by Professor Ted during the Spring '10 term at SUNY Albany.

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MTopic 1 - The IS Curve - Topic 1 The I-S Curve...

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