3. Suppose the supply curve for pizza is given by QS 6P, where QS is the quantit

Question

3. Suppose the supply curve for pizza is given by QS 6P, where QS is the quantity offered for sale when the prices is P. Also, suppose the demand curve for pizza is given by QD = 70-2P1, where QD is the quantity of pizza demanded when the price is P and the level of income is a) Find the equilibrium P and Q when 1 2 b) Find price-elasticity of demand at the equilibrium when I -2, and give an interpretation in terms of percents and classify the elasticity (elastic or inelas- tic c) Find the income-elasticity of demand at the equilib- rium when 1-2, and give an interpretation in terms of percents. What type of good is this (normal, infe- rye 0 rior, luxury) d) Find the equilibrium P and Q as a function of I e) Find the price elasticity of demand as a function of P and I and determine when this is unitary elastic. f) Find the income-elasticity in terms of P and I

Explanation / Answer

Supply is given by Qs = 6P and demand is given by Qd = 70 – 2PI.

a) For I = 2, find the equilibrium price and quantity by equating demand and supply

6P = 70 – 2*2P

10P = 70

P* = 7, Q* = 6*7 = 42.

This is the equilibrium price and quantity

b) Price elasticity of demand is given by = coefficient of price x current price/current quantity

ed = -4 x 7/42 = -0.66. Since absolute value of ed is 0.5 which is less than 1, demand is inelastic for price. For a 1 percent change in price, the quantity demanded will change by 0.66%

c) Income elasticity is given by = coefficient of income x current income/current quantity. When P is fixed at 7, demand is Qd = 70 – 2*7I or Qd = 70 – 14I

em = -14 x 2/42 = -0.66. Since income elasticity is negative, pizza is an inferior good. For a 1 percent change in income, the quantity demanded will change by 0.66%

d) Supply is given by Qs = 6P and demand is given by Qd = 70 – 2PI. Find the equilibrium price and quantity by equating demand and supply

6P = 70 – 2PI

P(6 + 2I) = 70

This gives P* = 70/(6 + 2I) and Q* 6 x 70/(6 + 2I) = 420/(6 + 2I)

e) Now the price elasticity is ed = -2 x [70/(6 + 2I)]/[420/(6 + 2I)] = -1/3. Since |ed| < 1, demand is inelastic

f) income elasticity of demand is ed = -2 x I/420/(6 + 2I) = -(6I + 2I^2)/210. Since income elasticity is negative, pizza is an inferior good.

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