PROBLEM #1 An economist, working for a public health agency, has estimated the s

Question

PROBLEM #1

An economist, working for a public health agency, has estimated the supply and demand equations for fast-food cheeseburgers in an urban area as follows:

Demand: Qd=2,450- 500P
Supply: Qs=200P


a. Determine the market equilibrium price and quantity for this market.

b. Calculate the price elasticities of demand and supply and, in each case,
determine whether it is elastic, inelastic, or unit elastic.

c. The public health agency is concerned with the rise in obesity, high blood
pressure, and diabetes, and persuades legislators to enact a $.75 tax per
cheeseburger. The revenues from the tax will be used to cover the cost of
advertising campaigns and educational programs to inform the public of the
potentially harmful effects from fast-food consumption. Under the new tax,
restaurants are required to submit $.75 to the government for every
cheeseburger sold. Find the new effective (out-of-pocket) price per
cheeseburger after the tax goes into effect. Determine the price received by
suppliers, per cheeseburger, net of the tax remitted.

d. Calculate the percentage burden that the consumers and producers each bear
of the new tax. Is your result consistent with the relative elasticities you
found in part b? Briefly explain.

Explanation / Answer

a. To find equilibrium, set supply equal to demand 200P=2450- 500P 700P=2450 P=3.5 Equilibrium is P=$3.50 and Q=700 b. Elasticity is s(P/Q), where s is the slope. Elasticity of demand is 500(3.5/700)=2.5 Elasticity of supply is 200(3.5/700)=1 So demand is elastic while supply is unit elastic. c. Let's treat this as a demand shift to the left (you could also treat it as a supply shift to the left and get the same answer). Setting supply equal to demand: 200P=2450- 500(P+0.75) 200P=2450-500P-375 700P=2075 Ps=$2.96 This is the price that the supplier gets to keep. Pd=2.96+0.75 Pd=$3.71 This is the price the consumers have to pay. It's always a good check to make sure the original price is between these. Q=2450- 500(3.71) Q=595 It's a good check to make sure that this is less than the original quantity. Keep in mind that this does not account for the demand decrease that will be produced by the advertising campaign. But we are not given enough information to incorporate that into our analysis. c. Consumers bear (3.71-3.5)/0.75 = 28% Producers bear (3.5-2.96)/0.75=72% It's always good to check that these add up to 100% and that the more elastic agents pay the less of the tax. Our result is consistent. Consumers are more elastic, so they pay less of the tax.

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