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.

No hand writing

Answer 1

At the equilibrium, we have:

QS = QD

i.e,

2p-2 = 13-p

3p= 15

P= 15/3 = 5

Therefore, Equilibrium Price = $5

Putting the value of equilibrium price in the expression for QS or QD, we get:

Q = 2(5)- 2= 10-2= 8

Therefore, Equilibrium Quantity = 8 millions of bushel

#Price elasticity of demand = |dQD/dP*(P/Q)|

= 1*(5/8)= 5/8= 0.625

Price elasticity of supply = |dQS/dP*(P/Q)|

=2*(5/8)= 5/4= 1.25

a) Since the equilibrium price is $5, which is below the price floor of $7, therefore, the producers will be willing to produce more but, the consumers will be willing to buy less at this new price and thus, leading to a surplus.

b) at the new price,

Quantity demanded = 13-7 = 6

Quantity supplied = 2(7)- 2= 14-2 = 12

Thus, quantity of excess supply = 12-6 = 6 mllion bushels.

The graph is given below