Question

Suppose that in a hypothetical economic setting, the demand curve is P=50-0.1Q and the supply curve is P=0.2Q+20 Find the equilibrium price and quantity. Compute the consumer and producer surplus in this hypothetical economic.

Answer 1

Solution:-

Consider the demand curve

P=50-0.1Q and ....(1)

Here, at Q = 0, P = 50 units

The supply curve

P=0.2Q+20 .....(2)

Here, at Q =0 , P = 20 units

Now, at the equilibrium point

Producer price = consumer price

So, 0.2Q + 20 = 50 - 0.1Q

Or 0.2W + 0.1Q = 50 - 20

Or 0.3Q = 30

Or Q = 30/0.3

Or Q = 100

Putting Q = 100 in equation (2), we get

P = 0.2(100) + 20 = 20+ 20 = 40

Hence,

Equilibrium price = P = 40 units

and Equilibrium quantity = Q = 100 units

Now, to compute the consumer and producer surplus in this hypothetical economic, we have drawn the demand curve and supply curve using the above information as shown below-

Now,

Consumer Surplus

= Area of ∆BCD

=(1/2)×(50-20)×100

= (1/2)×30×100

= 150

And

Producer Surplus

= Area of ∆ACD

=(1/2)×(40-20)×100

= (1/2)×20×100

= 100