Question

1) When the demand function is 2Q - 24 + 3P = 0, calculate the price elasticity of demand when P = 4 and find the marginal revenue when Q=3.

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

A: P= 35 - 0.5Q_A

B: P= 50 - 0.25Q_B

C: P= 40 - 2.00Q_C

The industry supply equation is given by Q_S = 40 + 3.5P

a) Determine the equilibrium price and quantity.

b) Determine the amount that will be purchased by each individual.

Answer 1

1)

2Q-24+3P=0

Q=12-1.5P

$P=8-\frac{2}{3}Q$

$\epsilon=\frac{dQ}{dP}×\frac{P}{Q}$

Where $\frac{dQ}{dP}=-1.5$

$\epsilon=-1.5×\frac{4}{6}$

$\epsilon=-1$

$MR=\frac{dTR}{dQ}$

$P=8-\frac{2}{3}Q$

$TR=P×Q$

$TR=8Q-\frac{2}{3}Q^2$

$MR=8-\frac{4}{3}Q$

2)

P=35-0.5Q_A ; Q_A=70-2P

P=50-0.25Q_B ;. Q_B=200-4P

P=40-2Q_C ; Q_C=20-0.5P

Q_s=40+3.5P

$E=Qd=Qs$

Where

$Qd=Q_A+Q_B+Q_C$

$Qd=290-6.5P$

$\therefore 290-6.5P=40+3.5P$

$250=10P$

$P^*=25$

$Q^*=290-6.5(25)=127.5$

$Q_A=70-2(25)$

$Q_A=20$

$Q_B=200-4(25)$

$Q_B=100$

$Q_C=20-0.5(25)$

$Q_C=7.5$