Question

Suppose demand and supply are given by Q^d = 50 - P and Q^s  = 0.5P - 10.

a. What are the equilibrium quantity and price in this market?

Equilibrium quantity:

Equilibrium price:

b. Determine the quantity demanded, the quantity supplied, and the magnitude of the surplus if a price floor of $48 is imposed in this market.

Quantity demanded:

Quantity supplied:

Surplus:

c. Determine the quantity demanded, the quantity supplied, and the magnitude of the shortage if a price ceiling of $34 is imposed in the market. Also, determine the full economic price paid by consumers.

Quantity demanded:

Quantity supplied:

Shortage:

Full economic price:

Answer 1

Answer:

* (a)

• Equilibrium quantity: 10

• Equilibrium price: $40  

* Explanation: Equating quantity supplied and quantity demanded yields the equation 50 - P = 0.5P - 10. Solving for P yields the equilibrium price of $40 per unit. Plugging this into the demand equation yields the equilibrium quantity of 10 units (since quantity demanded at the equilibrium price is Q d = 50 - (40) = 10).

• (b)

• Quantity demanded: 2

• Quantity supplied:14

• Surplus: 12

* Explanation: A price floor of $48 is effective since it is above the equilibrium price of $40. As a result, quantity demanded will fall to 2 units ( Q d = 50 - 48), while quantity supplied will increase to 14 units ( Q s = 0.5 (48) - 10). That is, firms produce 14 units but consumers are willing and able to purchase only 2 units. Therefore, at a price floor of $48, 2 units will be exchanged Since Q d < Q s there is a surplus amounting to 14 - 2 = 12 units

* (c)

• Quantity demanded: 16

• Quantity supplied: 7

• Shortage: 9

• Full economic price: $43

*Explanation : A price ceiling of $34 per unit is effective since it is below the equilibrium price of $40 per unit. As a result, quantity demanded will increase to 16 units ( Q d = 50 - 34 = 16), while quantity supplied will decrease to 7 units ( Q s = 0.5(34) - 10 = 7). That is, while firms are willing to produce only 7 units consumers want to buy 16 units at the ceiling price. Therefore, at the price ceiling of $34, only 7 units will be available to purchase. Since Q d > Q s , there is a shortage amounting to 16 - 7 = 9 units. Since only 7 units are available at a price of $34, the full economic price is the price such that quantity demanded equals the 7 available units: 7 = 50 – FEP . Solving yields the full economic price of $43.

**Thank you**