Introduction to Macroeconomics: Math App - Lecture 006

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Economics for Management Studies
Iris Au

23 January 2013 CHAPTER 21: AGGREGATED EXPENDITURE [CONT’D] Case 2: Initial Y > Y* (= 300) Suppose the initial Y = 360: When Y = 360, the level of AE = 100 + 2/3 (360) = 340 The adjustment mechanism when the output is less than 300: At Y = 360, there is excess supply (ES). Firms find their inventory has increased unexpectedly. The firms will then reduce production by reducing the amount of workers, and when the firms reduce production, income will also decrease. As workers lose their jobs, their income is 0. To calculate economy as a whole, we factor everyone’s income. The process continues until Y drops to 300. If Y < Y*  Excess Demand  Production ↑  Y↑ to Y* If Y > Y*  Excess Supply  Production ↓Y↓ to Y* The initial level of Y DOES NOT matter, the economy will always adjust itself and converge to Y* Exogenous Change in the AE Function Consider how an exogenous change in the AE function affects the equilibrium level of national income. The Multiplier (M) If AE increases by 1 unit, how much will Y* increase? 0 It depends on the size of the multiplier. The multiplier measures the change in equilibrium output or income (Y*) that results from a unit change in autonomous expenditure (AE ) 0 M = Y* / AE O AE = AE 0 C YY Y* = AE 0 1 / (1 – C Y M = Y* / AE = OY* / dAE = 1 O (1 – C ) Y If we take the partial derivative of Y* with respect to AE , we are holding 1 / (1 – C ) constant. 1 / (1 – C ) O Y Y is the derivative, also known as the multiplier. If the AE Oncreases by 1, then Y* increases by 1 / (1 – C ) Y and the size of the multiplier must be greater than 1 because 1 minus a fraction is another fraction and 1 divided by any fraction must be a value greater than 1. Since 1 > CY< 0, M > 1. The multiplier is greater than 1 because one’s expenditure = another’s income. Suppose AE ↑ by AE : 0 0 Round Change in AE Change in Y 1 AE ↑ by AE 0 Y ↑ by AE 0 2 C ↑ by C Y AE 0 AE ↑ further by C xYAE 0 Y ↑ further by C xYAE 0 3 C ↑ by C Y C xYAE 0 AE ↑ further by C xYAE 0 Y ↑ further by C xYAE 0 First Round For whatever reason you decided to spend a little bit more in the economy (AE ↑) by $10 (AE 0. 0 Buying coffee at Starbucks, it is true that you are spending $10 but through the Starbuck owner’s perspective it is their income, so his income goes up by $10; thus the total economy’s income (Y) has gone up by $10 (AE ). 0 Second Round The Starbucks owner understands their income has gone up by $10. The owner decides to spend a portion of his income on a book at Chapters (C). We assume households always spend a fraction of their income. The marginal propensity to spend on disposable income is 0.8 (C ). This means wYen the Starbucks owner receives the $10 (AE ), he 0pends $8 (C x AE ) oY books 0t Chapters. Through the perspective of Chapters the $8 (C x AE ) spent on the book is their income (Y). Y 0 Third Round The Chapters owner understands their income has gone up by $8. The owner decides to spend a portion of his income on a MacDonald
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