Question

The market for vanilla ice cream is given by the following information:

𝑄

𝑑 = 800 − 30𝑃

𝑣 + 10𝑃

𝑐

𝑄

𝑠 = 250 + 30𝑃

𝑣 − 10𝑃𝑚

Where 𝑄

𝑑

is the quantity demanded, 𝑄

𝑠

is quantity supplied, 𝑃

𝑣

is the price of vanilla ice

cream, 𝑃

𝑐

is the price of chocolate ice cream and 𝑃𝑚 is the price of milk. Let 𝑃

𝑐 = 10 and 𝑃𝑚 = 5. Calculate the equilibrium price and quantity in the vanilla ice 

cream market. Compare the own-price elasticity of demand and supply at equilibrium. (4

Answer 1

At equilibrium, supply is equal to demand. So;

$Qd=Qs$

$(800-30Pv+10Pc)=(250+30Pv-10Pm)$

We know that $Pc=10$ and $Pm=5$

hence; $800-30Pv+10(10)=250+30Pv-10(5)$

$30Pv+30Pv=800+100+50-250$

$Pv=12$ , which the price of Vanilla ice cream at equilibrium.

Therefore, quantity supplied at equilibrium is $250+30(12)-10(5)$

$=560$

The quantity demanded at equilibrium will be $(12)+10(10)$

$=540$