Answer to Question #201748 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. What happens if, starting from the position of equilibrium, the government imposes 2

price ceiling of Rs.2/-on commodity X? 

1. Should a producer, facing a negatively sloped demand curve for the commodity sold, operate in:

the inelastic range of the demand curve?

2. If the market demand for agricultural commodities is price inelastic, would a bad harvest

an increase or a decrease in the incomes of farmers (as. a group)?

Find the price elasticity of demand for the demand curve Q= ap-b?

3. The price elasticity of demand for a demand curve is the same for every level of p

of the demand curve would be Q=aP-b where a and b are the parameters of the curve?

Answer 1

Solution:

1.). First derive the market equilibrium price:

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

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

120,000 - 20,000P = 20,000P

120,000 = 40,000P

P = $\frac{120,000}{40,000} = 3$

P = 3

Equilibrium price = 3

The government price ceiling of Rs.2 is below the market equilibrium price of 3. A price ceiling set below the equilibrium price will result to quantity demanded exceeding quantity supplied and as such, excess demand or shortages will occur in the market.

 

1.). A producer who is facing a negatively sloped demand curve should not operate in the inelastic range of the demand curve. This is because by doing so, the producer would not be maximizing their profits effectively. The producer may reduce the price of the inelastic good, yet the demand for that particular good will remain constant hence reducing the overall revenue incurred by the producer since the reduction in prices does not change its demand.

2.). If the demand for agricultural commodities is price inelastic, a bad harvest will result to an increase in the farmers income. This is because a bad harvest is a result of crop failure and the farmers will not be able to harvest as much crops as they may want, which in turn will lead to massive shortages of commodities. This will cause the prices for those commodities to increase and since the demand for them will be higher, farmers will be able to sell them at higher prices and earn more incomes.

3.). Price Elasticity of demand (Ped) =$\frac{\%\;Change\;in\;quantity\;demanded}{\%\;Change\;in\;quantity\;price}$

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

Q = aP – b

Rearrange the demand curve:

Q = a – bP

Derive the inverse function:

P = a – b (Q)

Therefore:

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

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