Lecture3

# Lecture3 - LECTURE 3 Subsidies P S!tax S \$3 \$3 S!subsidy A...

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LECTURE 3 Subsidies: P S ! tax A per unit subsidy is simply the S \$3 S !! subsidy opposite of a per unit tax. The subsidy shifts the supply curve to the right since the producer’s costs have fallen and they are \$3 now willing to supply more at any given price level. Q As a good learning exercise, you might re-write the tax analysis (on the last few slides of lecture 2) within the context of a subsidy instead of a tax. We will return to an application of this concept in this class… Now that we have the theoretical knowledge, let’s put it to practical use by solving an example of a unit tax on producers…

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EXAMPLE: The supply and demand of concert tickets are given by the following equations: Q S = 3P Q D = 150 2P = 150 – 2P a) Solve for the equilibrium price and quantity. At equilibrium, we know that Q S = Q D . Since both of these equations are functions of P, we can solve for the equilibrium price (P*) and substitute this magical P* back into the supply and demand equations to find the equilibrium quantity. 3P = 150 – 2P 5P = 150 P*= 30 P 30 Sub P* = 30 into Q S = 3P and into Q D = 150 – 2P to obtain the Q*… Q S = 3P Q D = 150 – 2P Q S = 3(30) Q D = 150 – 2(30) Q* = 90 Q* = 90
EXAMPLE (continued): b) Calculate the price elasticity of demand and supply at the equilibrium. Denote the price elasticity of demand e d and the elasticity of supply as e s . Let’s begin with the demand equation, Q D = 150 – 2P and use the elasticity formula we learned earlier. e d = " Q D · P* " P Q* Notice that " Q D is simply the slope of the demand curve (i.e. the coefficient on P in the equation) and we’ve already solved P* and Q* and Q . e d = - 2 · 30 90 e d = - 60 90 e d = - 2/3 Next we deal with the supply equation Q S = 3P and use the elasticity formula Next, we deal with the supply equation, Q = 3P and use the elasticity formula we learned earlier. e s = " Q S · P* Notice that " Q S is simply the slope of the supply curve (i.e. the coefficient on P in the equation) and we’ve already solved P* " P Q* coefficient on P in the equation) and we ve already solved P and Q*. e s = 3 · 30 90 e s = 90 90 e s = 1

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EXAMPLE (continued): c) Use the elasticity figures from part b) and the following formula to calculate the increase in price for consumers that results from a \$5 per ticket tax on the producers of concert tickets. Assume that there was no prior tax in place before this tax was levied (i.e. " t = 5). ! P = __e s __ · ! t (e s –e d ) " P = __e s __ · " t (e s d ) " P= 1 · 5 The increase in the price (burden to consumers) is \$3 of the \$5 tax. This means that the producer can pass \$3 out of P = ____1 ____ 5 (1 – (-2/3)) " P = ____1 ____ · 5 This means that the producer can pass \$3 out of the \$5 on to consumers through a price increase. So the consumer pays 60% of the tax burden as opposed to the producer who only pays 40% 5/3 " P = (0.6) · 5 pays 40%. This result stems from the fact that supply is more elastic than demand and so producers will pay less than ½ of the tax ! P = 3 pay less than ½ of the tax.
EXAMPLE (continued): d) There is another way to find the price increase in part c) without the formula.

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## This note was uploaded on 03/24/2010 for the course ECON 201 taught by Professor Vandewaal during the Spring '09 term at Waterloo.

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Lecture3 - LECTURE 3 Subsidies P S!tax S \$3 \$3 S!subsidy A...

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