Question

1. Market demand is given as Q^d = 200 – 3P. Market supply is given as Q^s = 2P + 100. In a perfectly competitive equilibrium, what will be price and quantity?
   1. Price will be $20 and quantity will be 140.
   2. Price will be $50 and quantity will be 260.
   3. Price will be $100 and quantity will be 300.
   4. Price will be $140 and quantity will be 380.

Answer 1

answer- option a. Price will be $20 and quantity will be 140.

In a perfectly competitive equilibrium, quantity demanded is equal to quantity supplied. Market demand and market supply are  stated in terms of Q ( quantity).

Hence, we will equate quantity demanded=quantity supplied

Qd = Qs

200 – 3P= 2P + 100.

Adding 3P on both sides-

200- 3P+3P= 2P+100+3P

( note: -3P + 3P=0)

200= 100+5P

Subtracting 100 on both sides-

200-100= 100+5P-100

( note- 100-100=0)

100= 5P

Dividing both sides by 5-

100/5= 5P/5

20=P

Hence, Equilibrium price is $20.

Equilibrium quantity will be determined by substituting this value of price is equations of demand and supply. As equilibrium quantity is the quantity at which both buyers and sellers agree upon, equilibrium quantity will be same both in demand function and supply function.

Qd = 200 – 3P

substituting P=20

Qd= 200- 3 x 20

Qd= 200 - 60= 140

Now,

Qs = 2P + 100

Qs= 2x20 + 100

Qs= 40+100= 140

Hence, Equilibrium quantity is 140. We can see that equilibrium quantity calculated from market demand function and market supply function is same.

option b, c and d are incorrect as we can see from our calculations above that P=$20 and Q=140. All other options show price and quantity above equilibrium level.