Question

It turns out that a shortage has befallen Japan. Only 20 units are available.

The inverse demand function is still P = 108 - 1.2 Q.

(Inverse) supply is still P = 0.5Q + 40.

What is the total surplus now?

Answer 1

In free market equilibrium, demand equals supply.

108 - 1.2Q = 0.5Q + 40

1.7Q = 68

Q = 40

P = (0.5 x 40) + 40 = 20 + 40 = 60

A shortage indicates market price is lower than equilibrium price.

When Q = 20,

From demand function:

P = 108 - (1.2 x 20) = 108 - 24 = 84

From supply function:

P = (0.5 x 20) + 40 = 10 + 40 = 50 (Actual market price)

From demand function, when Q = 0, P = 108 (Vertical intercept of demand curve).

Consumer surplus (CS) = Area between demand curve & market price = (1/2) x [(108 - 50) + (84 - 50)] x 20

= 10 x (58 + 34) = 10 x 92 = 920

From supply function, when Q = 0, P = 40 (Vertical intercept of supply curve).

Producer surplus (PS) = Area between supply curve & market price = (1/2) x (50 - 40) x 20

= 10 x 10 = 100

Total surplus = CS + PS = 920 + 100 = 1020

=