Question

Suppose Emily and Juan are the only two ice cream cone (and undifferentiated product) buyers where their demand functions are QdEmily = 6 − 2p for p < $3 and QdJuan = 10 − 4p for p < $2.5, respectively. Also suppose that Robert and Anitra are the only suppliers of ice cream cone and the supply functions are QsAnitra = 8p − 8 for p > $1 and QsRobert = 3p − 1.5 for p > $0.50. Solve for the market equilibrium outcomes. (i.e. What is the equilibrium market price and quantity? How do much Emily and Juan consume?, How much do Anita and Robert produce? Solve for each individual.

Answer 1

For the demand side we have QdEmily = 6 − 2p for p < $3 and QdJuan = 10 − 4p for p < $2.5. Thus, we have the market demand as

• Qd = 16 - 6p for p < 2.5
• Qd = 6 - 2p for 2.5 < p < 3
• Qd = 0 for p > 3

For the supply side we have QsAnitra = 8p − 8 for p > $1 and QsRobert = 3p − 1.5 for p > $0.50. Thus we have the market supply as

• Qs = 11p - 9.5 for p > 1
• Qs = 3p - 1.5 for 1 > p > 0.50
• Qs = 0 for p < 0.50

Thus we have market equilibrium where

Qd = Qs

16 - 6p = 11p - 9.5

25.50 = 17p

p = 1.5 (Market price)

Q = 7 units (Market quantity)

QdEmily = 6 - 2*1.5 = 3 units

QdJuan = 10 - 4*1.5 = 4 units

QsAnitra = 8*1.5 - 8 = 4 units

QsRobert = 3*1.5 - 1.5 = 3 units