Question

STAT101 Assignments2

Problem 2

Suppose the market for corn is given by the following equations for supply and demand:

QS = 2p − 2 QD = 13 − p where Q is the quantity in millions of bushels per year and p is the price.

Calculate the equilibrium price and quantity.

Sketch the supply and demand curves on a graph indicating the equilibrium quantity and price.

Calculate the price-elasticity of demand and supply at the equilibrium price/quantity.

The government judges the market price is under expectations and announces a price floor equal to $7 per bushel.

Would there be a surplus or a shortage? What would be the quantity of excess supply or demand that results?

Use the graph to show you results.

Answer 1

Solution:

Given,

The demand equation is QD = 13 − P

The supply equation is QS = 2P − 2

where, Q is the quantity in millions of bushels per year and P is the price of brushels.

We know that at the equlibrium the quantity demanded = quantity supplied.

Therefore, QD = QS

=> 13 - P = 2P - 2

=> 13 + 2 = 2P + P

=> 3P = 15

=> P* = $5, is the equilibrium price.

Using P=5 in any of the two equations, say in the demand equation, we get the equlibrium quantity

Q* = 13 - 5

=> Q* = 8 millions of bushels per year, is the equilibrium quantity.

The following graph shows the demand curve DD, supply curve SS, the equilibrium point E, the equlibrium price P* and the eqilibrium quantity Q*.

Price elasticity is the degree of responsiveness of the quantity demanded or supplied of a commodity to the change in its price. The price elasticity of demand and supply can be obtained by taking the partial derivative of the demand equation and the supply equation, respectively, with respect to the price multiplied to the ratio of the actual price to quantity.

Therefore, the price elasticity of demand =

=

=

=

At the equilibrium price and quantity, the price ealsticty of demand =

= -0.625

This shows that the demand is price inelastic as the absolute elasticity is less than one and the commodity is a normal good because the elasticity is a negative value.

Similarly, the price elasticity of supply =

=

=

At the equilibrium price and quantity, the price ealsticty of supply =

=

= 1.25

This shows that the supply is price elastic because the value of elasticity is greater than one.

Now, suppose the government judges the market price is under expectations and announces a price floor equal to $7 per bushel.

A price floor is an externally imposed lower boundary on the price of a commodity in the market. Governments usually set up a price floor in order to make sure that the market price of a commodity does not fall below a level that would threaten the financial existence of producers of the commodity in the market. Price floors are always fixed at a price greater than the equilibrium price in order to make them effective.

In this case, the government has decided the price floor, PF, to be at $7 which is $2 more than the eqilibrium price. At price PF, consumer demand is 6 millions of bushels per year, which is less than Q* due to downward sloping demand curve, and producer supply is 12 millions of bushels per year, which is more than Q* due to upward sloping supply curve. After the establishment of the price floor, the market does not clear at $7, and there is an excess or surplus supply of 12 - 6 = 6 millions of bushels per year.

The producers are always better off as a result of the binding price floor if the price is fixed higher than equilibrium price as it makes up for the lower quantity sold while the consumers are always worse off as a result of a binding price floor because they must pay more than the equilibrium price for a quantity that is lower than the equilibrium quantity.

The following graph shows the effects of a price floor.