Question

 

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.

1. Calculate the equilibrium price and quantity.
2. Sketch the supply and demand curves on a graph indicating the equilibrium quantity and price.
3. Calculate the price-elasticity of demand and supply at the equilibrium price/quantity.

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

1. Would there be a surplus or a shortage?
2. What would be the quantity of excess supply or demand that results?
3. Use the graph to show you results.

Answer 1

Equilibrium is found by equating the demand and supply equations ie Qd= Qs

2p-2= 13-p

3p=15

p=$5

Equilibrium price is $5 and equilibrium quantity is given as 2(5)-2=10-2=8 million bushels per year

The equilibrium is given as E in the graph above.

Price elasticity of supply at the equilibrium is given as

Es= % change in quantity/ % change in price

= (change in Q/ Change in P)* P/Q ( slope of the curve= change in Q/ change in P)

= slope of Supply equation*P/Q

= 2*5/8= 1.25

Ed= % change in quantity/ % change in price

= (change in Q/ Change in P)* P/Q ( slope of the curve= change in Q/ change in P)

= slope of demand equation*P/Q

= (-1)*5/8

=(-)0.625

a) If the government imposes a price floor of $7, it would be binding. This is because the price floor is more than the market price. This would create surplus of the good. This is because since the price is higher, the suppliers would be willing to supply more and the buyers would be buying less. So there is excess supply.

b) The surplus is shown in the graph which is 12-6=6 million bushels.

Another way could be by putting $7 as the price in the equations of demand and supply such that

Qs= 2(7)-2=14-2=12

Qd=13-7=6

Surplus=12-6=6 million bushels

c)

The Pf is the price floor and surplus and curves are marked in the graph above.