Question

market consists of three people A, B and C whose individual demand equations are as follows:

A: P = 30 – 1.00QA

B: P = 30 – 1.33QB

C: P = 30 – 0.80QC

(i) What is the market demand equation?

(ii) If one has 60 units, what price should he charge to sell the entire units? Determine the quantity demanded from each market

(iii) If the industry supply equation is QS = 70 +2P, determine the equilibrium price and quantity.

Answer 1

(i) What is the market demand equation?

Lets express the demand functions in the forms of Q first.

$Qa = 30-P$

$Q_{b} = \frac{30-P}{1.33}$

$Q_{c} = \frac{30-P}{0.80}$

The market demand is the total of these individual demands

$Qa +Qb+Qc = \frac{95.82+1.066P}{1.064}$

The market demand is $Q_{D}=$ $\frac{95.82+1.066P}{1.064}$

If one has 60 units, what price should he charge to sell the entire units? Determine the quantity demanded from each market

If Qd = 60, What is P

$60 =$ $\frac{95.82+1.066P}{1.064}$

$P=30$

The Quantity for each market when P=30

$Qa = 30-30$

$= 0$

(iii) If the industry supply equation is QS = 70 +2P, determine the equilibrium price and quantity.

$\frac{95.82+1.066P}{1.064}= 70+2P$

$P= 20$ this is the equilibrium price

$Q = 70+2(20) = 110. units$