Introduction to Macroeconomics: Math App - Lecture 005

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University of Toronto Scarborough
Economics for Management Studies
Iris Au

21 January 2013 CHAPTER 21: AGGREGATED EXPENDITURE In any model for economics it must consist of 2 types of variables:  Exogenous Variables are the values are given, they are constants and we do not need to solve for them; However, external factors or shocks can change the values of these variables  Endogenous Variables are the values determined within the model, we need to solve for them Why do we want to develop a model that determines national income? Just like any market, the equilibrium level of income is determined by supply and demand. However, demand (desired or planned expenditure) is not always equal to supply (actual expenditure). Aggregate Demand (AD) = Desired (or planned) expenditure (what we intend or want to spend): AD = C + (INTENDED) I + G + X – IM Aggregate Supply = Actual expenditure = Actual national income (GDE): Y = GDE = C + (ACTUAL) I + G + X – IM The key difference is investment (I) in GDE includes unintended change in inventories while investment (I) in AD includes only intended investment. It is certainly true that every act of production generates income for us; however, not all of that income gets translated into demand for the output of firms. We want a model that has some positive relationship between the income generated by production and the demand that exists for that production. The Underlying Aggregate Expenditure (AE) Model The underlying model is given by: AE = AE 0 C YY AE = Aggregate or Planned Expenditure is the amount we intend to spend on goods and services AE 0 Autonomous Expenditure is the level of expenditure the economy will spend even if income is 0 (IE: If you lose your job, your income goes to 0, but you still need to pay for your food) CY= AE / Y = Marginal Propensity to Spend out of GDP, the change in aggregated expenditure for a unit change in income. 1 > C y 0, we divide our income between spending and saving. Y = GDP = Output = Income Solving for Equilibrium The equilibrium level of output, Y*, is the level of Y such that planned expenditure equals to actual expenditure. We must always equate our planned expenditure (AE) to our actual expenditure (Y). If you know the value of the autonomous expenditure and marginal propensity you can solve for the GDP. Equilibrium: Y = AE Y = AEO+ C y (1 – CY) Y = AE0 Y* = AE O (1 – C Y NOTE: You will see this generic form for the remainder of the term. A Simple AE Model There are several assumptions of the simple AE model:  It is a closed economy, there is no foreign sector, we do not trade or sell to them so because of that, exports (X) = 0 and imports (IM) = 0  There is no government, they do not consume anything so because of that, taxes (T) = 0, transfer (TR) = 0 and government spending (G) = 0  The model only consists of two sources of demand, consumption and investment NOTE: This is only temporary to make the equations simpler; we will add these factors in next week. Consumption Function Households spend a fraction of their disposable income (DI) on final goods and services. Holding all else constant, consumption is positively related to DI. A simple consumption function: C = C(DI) DI = Y – T + TR DI is an after tax income (IE: Every month Iris receives a salary from the university, represented by the Y (income). The moment she receives her salary, a chunk disappears because the government takes away income tax immediately, represented by the T (tax). For having a child at home, she receives some child care benefits from the government which raises the amount of money she can spend, represented by TR. The result is the after tax income she can spend in the given month). NOTE: C(DI) does NOT mean C multiplied by DI, it means that C is a function of DI C = C0+ C 1I C0= Autonomous consumption C1= C / DI, 1 > C 1 0 C1is our marginal propensity to consume out of disposable income. It tells us that if our disposable income goes up by 1 unit how much our consumption actually goes up (IE: If C1 = 0.6, then if our take home income goes up by $1 we spend $0.6 more and the remainder is to savings). NOTE: If T = 0 and
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