Answer to Question #249378 in Microeconomics for jly

Question

2. Suppose the market demand for a cup of cappuccino is given by QD =24 - 4P and the market supply for a cup of cappuccino is given by QS = 8P – 12, where P = price (per cup).

a. Graph the supply and demand schedules for cappuccino.

b. What is the equilibrium price and equilibrium quantity?

c. Calculate consumer surplus and producer surplus, and identify these on the graph. 

Answer 1

Solution:

a.). The supply and demand graph is as below.

 

 

 

b.). At equilibrium: QD = QS

QD = 24 – 4P

QS = 8P – 12

24 – 4P = 8P – 12

24 + 12 = 8P + 4P

36 = 12P

P = 3

Equilibrium Price = 3

Substitute to derive quantity:

QD = 24 – 4P = 24 – 4(3) = 24 – 12 = 12

Equilibrium quantity = 12

 

c.). Consumer surplus =$\frac{1}{2}\times (6 - 3) \times 12 = \frac{1}{2}\times (3 \times 12) = \frac{1}{2} \times36 = 18$

Producer surplus = $\frac{1}{2}\times (3 - 1.5) \times 12 = \frac{1}{2}\times (1.5 \times 12) = \frac{1}{2} \times18 = 9$ ½ x (3 –

The consumer and producer surplus have been displayed as per the below graph: