Answer to Question #150034 in Microeconomics for Bashir

Question

1. The demand curve for product X is given by
a) Find the inverse demand curve.
b) How much consumer surplus do consumers receive when Px= $35?
c) How much consumer surplus do consumers receive when Px= $25?
d) In general, what happens to the level of consumer surplus as the price of a good falls?

Answer 1

The demand curve for product X is given by $Q^d_x = 460 - 4P_x$

a) Find the inverse demand curve.

b) How much consumer surplus do consumers receive when Px= $35?

c) How much consumer surplus do consumers receive when Px= $25?

d) In general, what happens to the level of consumer surplus as the price of a good falls?

a) Solve the demand function for P_x to obtain the following inverse demand function:

$P_x = 115 - \frac{1}{4}Q^d_x$

b) $P_x = 35$

$Q^d_x = 460 – 4 \times 35 = 320 \;units$

Also, from part a, we know the vertical intercept of the inverse demand equation is 115.

Consumer surplus = 0.5(115-35)320 = 12800

Thus, the consumer surplus is $12,800.

c) When the price decreases to $25, the quantity demanded increases to 360 units.

Consumer surplus = 0.5(115-25)360 = 16200

So, consumer surplus increases to $16,200

d) So long as the law of demand holds, a decrease in price leads to an increase in consumer surplus and vice versa. In general, there is an inverse relationship between the price of a product and consumer surplus.