Question

4) Consider the following demand for barrels of pretzels: Q_D=100-2P+4P_Chips-2P_NachoCheese+Income

a. Are pretzels a normal or inferior good?

b. What kind of related good are chips?

c. What kind of related good is nacho cheese?

d. Let P_Chips =2, P_NachoCheese =2, and Income=100. What is the demand curve?

e. Let the quantity supplied of pretzel barrels be Q_S=-20+5P. Solve for the market equilibrium price and quantity.

Answer 1

(a)

A good is a normal good if increase in income results in Increase in demand.

Here, Q_D=100-2P+4P_Chips-2P_NachoCheese+Income

This dQ_D/dIncome = 1 > 0 which means as income increases Q_D will increase.

Hence, as income increases demand of pretzels increases => Pretzel is a Normal Good.

(b)

Two goods are substitute goods if increase in price of one results increase in demand of other.

Here, Q_D=100-2P+4P_Chips-2P_NachoCheese+Income

This dQ_D/dP_chips = 4 > 0 which means as Price of chips increases Q_D will increase.

Hence, as price of chips increases demand of pretzels increases => Pretzel is a Substitute Good.

(c)

Two goods are complemantary goods if increase in price of one results decrease in demand of other.

Here, Q_D=100-2P+4P_Chips-2P_NachoCheese+Income

This dQ_D/dP_Nachocheese = -2 < 0 which means as Price of Nachocheese increases Q_D will decrease.

Hence, as price of chips increases demand of pretzels increases => Nachocheese and Pretzel is a Complementary Good.

(d)  Let P_Chips =2, P_NachoCheese =2, and Income=100

Also Q_D=100-2P+4P_Chips-2P_NachoCheese+Income

=> Q_D=100-2P+4_*2-2*2+100

=> Q_D = 204 - 2P ------------Demand curve

(e) AT equilibrium Demand = supply

=> 204 - 2P = -20+5P

=> P = 32. Hence equilibrium price = 32

Q = 204 - 2*32 = 140.-------------------Equilibrium quantity = 140