Answer to Question #201747 in Microeconomics for Nitin

Question

There are 10,000 identical individuals in the market for commodity X, each with a demand

function Q = 12—2P, where Q is the quantity of X demanded and P is the price of X, and 1,000

identical producers of commodity X, each with a supply function given by Q=20P, where Qis —

quantity of X supplied and P is the price of X.

a. Find the market demand and market supply function for commodity X.

b. Obtain the equilibrium price and equilibrium commodity of X.

c. Calculate the own-price elasticity function (in terms of price) for both the market

demand curve and the market supply curve. Using these functions, calculate the

own-price elasticity of demand and supply at the point of equilibrium.

d. Calculate the consumer surplus and the producer surplus at equilibrium?

e. What happens if, starting from the position of equilibrium, the government imposes 2

price floor of Rs.4/- on commodity X?

Answer 1

Solution:

a.). Market demand:

Individual demand: Q = 12 – 2P

Market demand function: Q = 10,000(12 – 2P) = 120,000 – 20,000P

Individual supply: Q = 20P

Market supply function: Q = 1000(20P) = 20,000P

 

b.). At equilibrium: Quantity demanded (Q_d) = Quantity supplied (Q_s)

120,000 – 20,000P = 20,000P

120,000 = 20,000P + 20,000P

120,000 = 40,000P

P = 120,000/40,000

P = 3

Equilibrium price = 3

Equilibrium commodity: Substitute price in the market supply function or the market demand function:

Market supply function = 20,000P) = 20,000(3) = 60,000

Equilibrium commodity = 60,000

 

c.). Price Elasticity of demand (Ped) = % change in quantity demanded / % change in price

Price Elasticity of Supply (PEs) = % change in quantity supplied / % change in price

PEd = $\frac{\triangle Q}{\triangle P}\times \frac{P}{Q}$

Price elasticity function:

Q = a – bP

Derive the inverse function:

P = a – b (Q)

Therefore:

Price Elasticity of demand (PEd) = $\frac{\triangle Q}{\triangle P}\times \frac{P}{Qd} = -b\times\frac{P}{Qd}$

Price Elasticity of Supply (PEs) = $\frac{\triangle Q}{\triangle P}\times \frac{P}{Qs} = -b\times\frac{P}{Qs}$

At equilibrium: PEd = PEs

Market demand curve = 120,000 – 20,000P

Equilibrium price = 3

Equilibrium quantity = 60,000

Price Elasticity of demand and Supply (PEd) and PEs = -20,000 * 3/60,000 = -0.001

d.). Consumer surplus at equilibrium:

Consumer surplus = $\frac{1}{2}\times (3\times20,000) = 30,000$

Producer surplus = $\frac{1}{2}\times (3\times60,000) = 90,000$

e.). The price floor has been set above the equilibrium price of 3. When a price floor is set above the equilibrium price, quantity supplied will exceed quantity demanded, and excess supply or surpluses will result.