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Juan’s demand function for ice cream cones is QdJuan = 10 2.5P at prices below $

ID: 1111397 • Letter: J

Question

Juan’s demand function for ice cream cones is QdJuan = 10 2.5P at prices below $4 and zero at prices above $4. Emily’s demand function is QdEmily = 6 1.5P at prices below $4 and zero at prices above $4. Anitra’s supply function for ice cream cones is QsAnitra = 6P 4 at prices above $0.67 and zero at prices below $0.67. Robert’s supply function for ice cream cones is QsRobert = 4P 8 at prices above $2 and zero at prices below $2. What are the market equilibrium price and amount bought and sold given these individual demand and supply curves? What are the aggregate surplus, consumer surplus, and producer surplus at the competitive market equilibrium?

Explanation / Answer

Market demand is the sum of individual demands. It is given by

QD = 16 - 4P for price level 0 < P < 4 and

QD = 0 for P > 4

Market supply is not a straight line. It is given by

QS = 0 for P < 0.67

QS = 6P 4 for 0.67 < P < 2

QS = 10P - 12 for P < 2

Market equilibrum is found to be

QD = QS

16 - 4P = 10P - 12

28 = 14P

P* =2

Q* = 8 units

At equilibrium only Anitra is supplying but demand is made by both Juan and Emily

Consumer surplus = 0.5*(4 - 2)*8 = $8

Producer surplus = 0.5*(2 - 0.67)*8 = 5.32

Aggregate surplus = 8 + 5.32 = 13.32