Question

Consider the market for education. 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

• When PT = $10 and PB = $50, then supply curve is 100PE - 500 and demand curve is 1000 - 150PE + 5000 which makes 6000 - 150PE. At equilibrium demand = supply, thus 100 PE - 500 = 6000 - 150 PE, which makes PE = 22.

Putting this PE in either demand or supply equation gives quantity as 1700.

• When PT = 20 and PB = 50, supply curve is 100 PE - 1000 and the demand curve is 6000 - 150 PE. At equilibrium, 100 PE - 1000 = 6000 - 150 PE, thus PE = 28.

Putting this price in demand or supply equation gives 1800 as quantity.

• When PE = 50, there would be excess supply in the market. Put PE = 50 in demand equation, 6000 - 150 * 50 = 1500  

Put PE in supply equation, 100 * 50 - 500 = 4500

Thus there is excess supply of 3000 units.

When PE = 20, there would be excess demand

Put PE in demand equation, 6000 - 150 * 20 = 3000

Put PE in supply equation, 100 * 20 - 500 = 1500

Thus excess demand is of 1500 units.