Question

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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.

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

Setting QD = QS,

13 - p = 2p - 2

3p = 15

p = 5

Q = 13 - 5 = 8

Elasticity of demand = (dQD / dp) x (p / QD) = - 1 x (5/8) = - 0.625

Elasticity of supply = (dQS / dp) x (p / QS) = 2 x (5/8) = 1.25

From demand: When QD = 0, p = 13 and when p = 0, QD = 13.

From supply: When QS = 0, p = 2/2 = 1.

In following graph, D0 and S0 are demand and supply curves, intersecting at point E with equilibrium price P0 (= 5) and quantity Q0 (= 8).

When p = 7,

QD = 13 - 7 = 6

QS = 2 x 7 - 2 = 12

Since QD < QS, there is a surplus equal to (QS - QD) = 12 - 6 = 6.

In the graph, at price of P1 (= 7), quantity demanded is lower at QD and quantity supplied is higher at QS, causing surplus of (QS - QD).