Question

In this market the supply curve is given by Qs= 100Pe – 50Pt and the demand curve is given by Qd = 1000 – 150Pe + 100Pb, where Pe denotes daily price of education tuition, Pt denotes teacher wage per hour, and Pb denotes price of textbooks.

a) Assume that Pt is fixed at $10 and Pb = $50. Calculate the equilibrium price and quantity. Illustrate this market using a supply and demand diagram.

b) Suppose the teacher’s union successfully lobbies for higher wages and Pt rises to 20. Find the new equilibrium price and quantity of education. Copy the graph from (a) and illustrate the changes on this new graph.

c) Suppose Pt = $10 and Pb= $50 and there is a price ceiling on education of Pe = $50. Will this cause excess supply or demand? How much excess? Draw a graph to illustrate your answer. What about a price ceiling of Pe = $20?

Answer 1

(a) Plugging in given values,

Qd = 1000 - 150Pe + (100 x 50) = 1000 - 150Pe + 5000 = 6000 - 150Pe

Qs = 100Pe - (50 x 10) = 100Pe - 500

In equilibrium, Qd = Qs.

6000 - 150Pe = 100Pe - 500

250Pe = 6500

Pe = $26

Q = (100 x 26) - 500 = 2600 - 500 = 2100

From demand function,

When Qd = 0, Pe = 6000/150 = $40 (Vertical intercept) & when Pe = 0, Qd = 6000 (Horizontal intercept).

From supply function,

When Qd = 0, Pe = 500/100 = $5 (Vertical intercept).

In following graph, D0 & S0 are demand and supply functions intersecting at point A with price P0 (= $26) and quantity Q0 (= 2100).

(b) When Pt = $20,

Qs = 100Pe - (50 x 20) = 100Pe - 1000

Equating with Qd,

6000 - 150Pe = 100Pe - 1000

250Pe = 7000

Pe = $28

Q = (100 x 28) - 1000 = 2800 - 1000 = 1800

From new supply function,

When Qd = 0, Pe = 1000/100 = $10 (Vertical intercept).

In above graph, D0 & S1 are demand and new (left-shifted) supply functions intersecting at point B with price P1 (= $28) and quantity Q1 (= 1800).

(c) When ceiling price is $50, this is higher than equilibrium price of $26. A price ceiling is effective only when it is imposed lower than equilibrium price. So in this case the ceiling price is non-effective and market equilibrium will remain unchanged at Pe = $26 and Q = 2100.

In following graph, ceiling price is Pc (= $50) at which price and quantity remain unchanged at P0 (= $26) and Q0 (= 2100).