Question

1. Elasticities Consider the following supply and demand functions AD = 16-4p Is2 +5p a) Plot the supply and demand functions. b) What are the equilibrium price and quantity? c) At the equilibrium price and quantity, what is the price elasticity of demand? d) Interpret the price elasticity of demand. How much will quantity change if the price increases by 1%? e) Suppose I were to calculate an income elasticity of 0.1. What does this imply about the good in our market? f) Suppose there were another good in our market and I calculated a cross-price elasticity of e1.65. What does this imply about the relationship between both goods?

Answer 1

a) Demand: p = 4-0.25qd
Supply: p = 0.4+0.2qs

Green: supply
Red: demand

아 (0.4) (8, 2) (0,0.4) (16,0) -2 02 4 68 10 12 14 16 T8 20 24 -2

b) equilibrium price = 2, equilibrium quantity=8

c) price elasticity of demand = %change in quantity/ % change in price
= dqd/qd / dp/p
= dqd/dp * p/q
= -4*2/8 = -1

d) If the price increases by 1%, quantity decreases by 1% as price elasticity of demand = %change in quantity/ % change in price => %change in quantity = %change in price * price elasticity of demand

e) A positive income elasticity of demand being less than 1 implies that it is a necessity good. This means that people will buy these items irrespective of the income and an increase in income will bring about less than proportionate increase in quantity demand.

f) Positive cross price elasticity implies that the goods are substitutes as cross-price elasticity of demand = %change in quantity_x/ % change in price_y => %change in quantity_x = %change in price_y * price elasticity of demand i.e. if the price of the other item increases, the quantity demanded of the good icreases