Answer to Question #285313 in Microeconomics for evans

Question

Campbell owns an online shop and to sell to three (3) individuals, A, B and C, whose individual demand equations are as follows:

•     A: P = 70 -1.0Q_A

•     B: P = 100 -0.5Q_B

•     C: P = 80 -4.00Q_C

The industry supply equation to be Q_S = 80+ 7P

You are required to 

a.      Determine the equilibrium price and quantity 

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

Answer 1

We will first convert the three demand equations into the format Qd=x-yP.

A: Qa=70-P

B: Qb=200-2P

C: Qc=20-0.25P

We will now add the three demand equations above to determine the total demand.

70-P+200-2P+20-0.25P=290-3.25P

Our total demand function is now Qd=290-3.25P and our supply function is 80+7P

At equilibrium, quantity supplied is always equal to quantity demanded therefore:

80+7P=290-3.25P

7P+3.25P=290-80

10.25P=210

P=20.49

If we substitute the value of P to the quantity supplied or quantity demanded equation, we find that the value of Q=223.43

Therefore 20.49 is the equilibrium price and 223.43 is the equilibrium quantity.

B. To now determine the amount that will be purchased by each individual, we will substitute the value of P to each individuals equation as shown below:

A: 70-20.49=49.51

B: 200-2(20.49)=159.02

C: 20-0.25(20.49)=14.88

Therefore individual A will purchase 49.51 quantities, B 159.02 and C 14.88 quantities.