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Unformatted text preview: PADP 6950 Fall 2011
Fertig UGA Homework 3 Solutions Assume that the demandfar Cigarettes is Qd=1 600—30P and the supply of
cigarettes is Q321400+70R 1. Calculate the equilibrium price and quantity and Show them on a supply
and demand diagram. Qd:QS 1600—30PE1400+70P
200=100P P=2 Q21600—30*2 Q=1540 Equations for graphing D: Q21600-30P
P=53.33-[1/30)Q S: Q=1400+70P
' i—I O H N (J0 >53 U1 0‘ \J 2. Suppose the government levies a $2 tax for each unit of cigarettes sold. Draw this
on the diagram and calculate the new equilibrium price and quantity. Demand curve shifts down by $2 — new equation is P=51.33-[1/30)Q.
Set this equal to supply and solve for Q.
~204-(1/70)(25:13133-[1/30]Qd (1/70)Q+[1/30)Q=51.33+20 [10/210)Q271.33 Q:1497.93
P=S 1.33—(1/30)*1497.93=1.40 (supplier’s pin-ice;- the-consumer's price is $3.40)” .. 3. Calculate the price elasticity of demand given these two price and quantity points.
is the demand for cigarettes price elastic or inelastic on this part of the demand curve? interpret the elasticity in words ( i. e, if the prices rises by 10%, by what
percentage will consumption fail?) 1.497 9% —42.07
_ ”W2 W 1518965 _ —o.027 _ ,
Tl _ %AP _ ﬂ; 4 ﬂ ~ ”(J-g5 ~ #0053 Inelastic (<1)
(3.40+2)i2 27 Ifthe price rises by 10%, consumption will fail by 0.5%. 4. On a graph, identijj/ the tax revenue generated by this tax. l “HS
5. Indicate each area on the graph with a letter and Show in a table the consumer
surplus and the producer surplus before and after the tax. Also indicate the dead weightless associated with this tax. A+ B +C A -C
' The deadweight loss if —C-E. 6. ifyaur policy advisor boss wantedyou to provide him/her with arguments in favor
ofthis cigarette tax, what would you say? It should raise a Eot of tax revenue since consumption is high and will not change
much as a result ofthe tax. While not shown here, the elasticity of younger smokers is much higher so it will
reduce the number ofnew smokers. 7. ifyour policy advisor boss wantedyou to provide him/her with arguments against
this cigarette tax, what wauidyou say? The tax will have littie effect on cigarette consumption on average.
The tax distorts the market resulting in deadweight toss [a iack of efficiency). Consumers wili bear most of the burden ofthe tax with iarge losses in consumer
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- Spring '11