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MPC, MPS, and Multipliers • Any increase in spending will result in an even larger increase in GDP due to the fact that every dollar spent is spent again multiple times. • Any money spent is someone else’s income and therefore subject to spending. Decisions to Save and Spend • How strong the multiplier effect will be is determined by our decisions to save and spend. • As our income changes we will spend a portion and save a portion of this change. Marginal Propensity to Consume • The portion we spend is known as our Marginal Propensity to Consume (MPC) • It is found by dividing the change in Consumption by the change in Disposable Income • For example if we receive a $10 an hour raise and we spend $9 of it and save $1, then our MPC is .9 C/ DI = MPC so 9/10 = .9 Marginal Propensity to Save • The portion we save is known as our Marginal Propensity to Save (MPS) • It is found by dividing the change in Savings by the change in Disposable Income • For example if we receive a $10 an hour raise and we spend $9 of it and save $1, then our MPS is .1 S / DI = MPS so 1/10 = .1 • The MPC + MPS is always equal to 1 • The limiting factor for the multiplier effect is savings. • For every additional dollar spent a portion of it will be saved (the MPS). • The multiplier is the reciprocal of the MPS or 1/MPS or 1/1- MPC. • The larger the MPC (the smaller the MPS) the larger the multiplier will be. Spending Multiplier = 1/MPS MPC .90 .80 .75 .60 .50 1/MPS 1/.10 1/.20 1/.25 1/.40 1/.50 = M = 10 = 5 = 4 = 2.5 = 2 The First Round of Government Spending Causes The Biggest Splash MPC of 75% G spends $200 billion on the highways. Highway workers save 25% of $200 billion [$50 billion] & spend 75% or $150 billion on boats. Boat makers save 25% of $150 bil. [$37.50 bil.] & spend 75% or $112.50 bil. on iPod Minis, etc. Total Saving has reached $87.50 USING MULTIPLIERS • The multiplier can be used to calculate how any change in spending will change total spending (AD) or income (GDP). • The formula used is: Change in Spending x Multiplier = Change in AD/GDP. • Ex: G $1b x 4 = $4b in AD/GDP USING MULTIPLIERS • Since any change in GDP is the result of the change in spending x multiplier, you can find the multiplier by dividing the change in AD/GDP by the change in spending. • Ex: $4b AD/GDP / multiplier of 4 $1b in G = USING MULTIPLIERS • Knowing that any change in spending will have a multiplied effect government can calculate how much to change spending by dividing the needed change in GDP by the multiplier. • Ex: GDP is $4b below full employment $4b needed / 4 = $1b in G • A change in taxes also has a multiplied effect, but the tax multiplier is smaller than the spending multiplier. • Tax Multiplier (note: it’s negative because tax increases reduce spending) -MPC/ or MPC/ 1-MPC MPS • If there is a tax-CUT, then the multiplier is +, because there is now more money in the circular flow Tax Multiplier = -MPC/MPS MPC .90 .80 .75 .60 .50 = M -MPC/.10= -9 -MPC/.20= -4 -MPC/.25= -3 -MPC/.40= -1.5 -MPC/.50= -1 MPC/MPS Spending Multiplier = 1/MPS Multiplier MPC .9 5 .75 4 -3 Tax Multiplier -9 10 .8 Tax Multiplier = -MPC/MPS -4 .60 2.5 -1.5 .5 2 -1 The tax multiplier is always smaller than the spending multiplier because a portion of the change in income due to taxes is saved, reducing the overall impact on spending. The Balanced Budget Multiplier • When government spending increases are matched with equal size increases in taxes, the change ends up being = to the change in government spending • Why? • 1/MPS + -MPC/MPS = 1- MPC/MPS = MPS/MPS = 1 • The balanced budget multiplier always = 1 Multiplier Practice • Assume US citizens spend $.90 for every extra $1 they earn. • Further assume that the real interest rate (i) decreases, causing a $50 billion increase in Investment (I). • Calculate the effect of this increase in spending on AD. Step 1: Calculate the MPC and MPS MPC = C / DI MPS = 1- MPC = Step 2: Determine which multiplier to use, and whether its + or – The problem mentions an increase in I, use a (+) spending multiplier Step 3: Calculate the Spending and/or Tax Multiplier Step 4: Calculate the Change in AD ( C, I, G or NX) * Spending or Tax Multiplier More Practice • Assume Germany raises taxes on its citizens by 200b. • Assume that Germans save 25% of the change in their disposable income. • Calculate the effect of these taxes on the German economy. More Practice • Assume the Japanese spend 4/5 of their disposable income. • Assume that the Japanese government increases its spending by 50 trillion and in order to maintain a balanced budget simultaneously increase taxes by 50t. • Calculate the effect of these changes on the Japanese Aggregate Demand.