Question

The supply and demand for organic peanut butter are QD = 70 – 5P and QS = 5P, where P is price per jar and Q is in hundreds of jars per day. The government has two pieces of legislation up for debate: a $1 supply subsidy or a price floor equal to $7.50. Defend your answers with math and economic logic! No defense means no credit. A) Which law would be more efficient (i.e. result in less deadweight loss)? B) Which law would producers most likely vote for? C) Which law would consumers most likely vote for?

Answer 1

QD = 70 – 5P

P	0	14
QD	70	0

Here Price when Quantity demand is zero Po= 14

QS = 5P

Here Price when Quantity supply is zero Po'= 0

Equilibrium:

QD=QS

70-5P=5P

P*= 7

Q*= 35

Consumer surplus	Producer surplus	Total surplus
1/2(Po-P*)(Q*)=122.5	1/2(P*-Po')(Q*)= 122.5	122.5+122.5= 245

If government provide $1 supply subsidy it will cause supply curve to shift right from SS1 to SS2 and for new equilibrium:

QS' = 5(P+1)= 5P+5

Equilibrium:

QD=QS'

70-5P=5P+5

P**= 6.5

Q**= 37.5

Consumer surplus	Producer surplus	Total surplus
Area (a+b+c+d)= 1/2(Po-P**)(q**)= 140.625	Area (d+e+f)= 6.5 x 37.5 - 1/2 (37.5-5)(6.5) =243.75-105.625= 138.125	140.625+138.125= 278.75

In this situation there is no deadweight loss because total surplus increases by 33.75 and also producer surplus increases by 15.625 and consumer surplus increases by 18.125.

If government Price floors equals to $7.5

P**= 7.5

QD = 70 – 5P= 70-5(7.5)= 32.5

QS= 5x7.5= 37.5

Consumer surplus	Producer surplus	Total surplus
Area (a)=1/2(Po-P**)(QD) = 105.625	Area (b+d) + area f= 1 x 32.5 + 1/2(P**-P0')(32.5) = 138.125	105.625+138.125= 243.75

In this situation there is deadweight loss because total surplus decreases by 1.25 and also producer surplus increases by 15.625 and consumer surplus decreases by 16.875.

A) It is more efficient to use law to provide supply subsidy because it cause no deadweight loss even it cause rise in total surplus.

B) For producer the surplus is increasing by the same rate so producer will be indifferent between the two laws.

C) For consumer, Surplus increases by 18.125 when supply subsidy was used and when price flooring used consumer's surplus decreases by 16.875 so consumer will vote for supply subsidy.