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Q: Macroeconomics ( Answered,   0 Comments )
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 Subject: Macroeconomics Category: Business and Money Asked by: cloudbasepilot-ga List Price: \$20.00 Posted: 16 Apr 2006 18:45 PDT Expires: 16 May 2006 18:45 PDT Question ID: 719583
 ```OK, I'm stuck on this question if anyone can help me work through it. Suppose the government decreases spending by \$20 billion. How much will this change equilibrium GDP if the MPC is 80 percent and the tax rate is 1/6 (16.6 percent)?```
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 Subject: Re: Macroeconomics Answered By: livioflores-ga on 17 Apr 2006 10:02 PDT
 ```Hi!! First remember that change in equilibrium GDP equals the change in total government spending times the multiplier: change in GDP = (change in spending) * (multiplier) How the multiplier works? Suppose the MPC for everybody is 0.8, this means that for every dollar someone gets he will spend 80 cents and save 20 cents. If you buy something and pay \$100, the seller gets \$100 and then he will spend \$80=(0.8*\$100) in another thing; the second seller will spend 0.8*(0.8*\$100); the third seller will spend 0.8*(0.8*(0.8*\$100)); etc. The increase in total spending in this case will be: \$100 + (0.8*\$100) + (0.8^2*\$100) + (0.8^3*\$100) + ... = = \$100 * (1 + 0.8 + 0.8^2 + 0.8^3 + ...) = = \$100 * (1/(1-0.8)) = this is a geometric series that converges according to a known formula, then you will get the following result: change in GDP = change in spending * (1/(1-MPC)) = Then the multiplier is equal to (1/(1-MPC)) We found the formula without considering the taxes, if the taxes are related to the income then if you get \$100 you must save for taxes T*\$100, and from the resulting amount, (1-T)*\$100, you will spend MPC*(1-T)*\$100, and the chain continues in the same mode than the above example and the new factor in the formula is MPC*(1-T), so the new multiplier is: (1/(1-MPC*(1-T)) Using the above result on your problem we have: change in spending = -\$20 billion MPC = 0.8 T = 1/6 Multiplier = 1 / (1 - 0.8*(1-1/6) = = 1 / (1 - 0.8*5/6) = = 1 / (1 - 2/3) = = 1 / (1/3) = = 3 change in GDP = (change in spending) * (multiplier) = = -\$20 billion * 3 = = -\$60 billion The GDP will decrease by \$60 billion. For further references see the following pages: "PRINCIPLES OF MACROECONOMICS - Lectures, Week 11": Read the paragraph II. THE MULTIPLIER MODEL. http://www.oswego.edu/~dighe/lstums11.htm "Multipliers": See at the bottom of page 2 "The Multiplier with taxes". http://www.econ.umn.edu/~aevk/pdfs/teaching/2005spring/1102notes1corr.pdf Search strategy: gdp mpc tax formula Government Spending mpc tax gdp I hope this helps you. Feel free to use the clarification feature if you find something unclear or incomplete. I will gladly respond your requests for further assistance on this question. Regards, livioflores-ga```
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