Question

1. Suppose Q D = 200 – 4P and Q S = 100 describe market demand and market supply in a given market.

1. Find the equilibrium price and quantity for this market.
2. Graph both supply and demand for this market.
3. Compute the consumer and producer surplus for this market.
4. Give an example of a good in the real world that might be described by this graph

Answer 1

(a)

In equilibrium, QD = QS.

200 - 4P = 100

4P = 100

P = 25

Q = 100

(b)

From demand function, when QD = 0, P = 200/4 = 50 (vertical intercept) & when P = 0, QD = 200 (horizontal intercept).

In following graph, D0 and S0 are demand and supply functions intersecting at point A with price P0 (= 25) and quantity Q0 (= 100).

0 100 200

(c)

Consumer surplus = area between demand curve and price = (1/2) x (50 - 25) x 100 = 25 x 50 = 1250

Producer surplus = infinity (since quantity is fixed and price is completely flexible)

(d)

An example will be Land in the local town, since its available quantity will be fixed. Higher demand will only increase its price but quantity will not change.