Question

Chapter 6, Section 6.4, Question 006 

The demand and supply curves for a product are given as 

q-4p = -26 

q+2p= 34. 

Enter the exact answers.

 (a) Find the consumer surplus at the equilibrium. 

Consumer surplus = $_______ 

 (b) Find the producer surplus at the equilibrium 

 Producer surplus = $_______ 

Answer 1

Answer 2

SOLUTION :

Supply curve :  (It has positive slope).

q - 4p = - 26 

=> p = 1/4 q + 6.5  (it is supply curve as slope is positive)

Demand curve : (It has negative slope).

q + 2p = 34

=> p = - 1/2 q + 17 (it is a demand curve as its slope is negative)

At equilibrium, p demand = p supply.

So,

1/4 q + 6.5 = - 1/2 q + 17

=> 3/4 q = 10.5

=> q = 14

=> q equilibrium  = 14 

=> p equilibrium = 1/4 * 14 + 6.5 = 10 ($)

a.

At q = 0, p maximum = 17 ($)  (as per demand curve equation : p = - 1/2 q + 17 )

So,

Consumer surplus at equilibrium :

= area under demand curve above equilibrium price of $10

= 1/2 * (maximum price - equilibrium price) * equilibrium quantity

= 1/2 * (17 - 10) * 14

= 49 ($) (ANSWER).

b.

At q = 0, p minimum = 6.5 ($) ( as per supply equation : p = 1/4 q + 6.5)

So,

Producer surplus at equilibrium

= area under supply curve below equilibrium price

= 1/2 * (equilibrium price - minimum price) * equilibrium quantity

= 1/2 * (10 - 6.5) * 14

= 24.5 ($)  (ANSWER).