Question

The demand equation for a manufacturer's product is:

Answer 1

From the given price function, we have;

(a) $\frac{dp}{dq} = - 13$

(b) The point elasticity of demand is 0.0256; inelastic demand

(c) $46.6

(d) Increase

How can the elasticity of demand be found?

a. The given function is presented as follows;

$p = 50 \times (151 - q) ^{0.02 \times \sqrt{q + 19} }$

Differentiating the above function with a graphing calculator and setting q = 150 gives;

$\frac{dp}{dq} = - 13$

b. The point elasticity of demand is given by the formula;

$e \: = \frac{dq}{dp} \times \frac{p}{q}$

When q = 150, we have;

P = 50

Which gives;

$e \: = \frac{1}{13} \times \frac{50}{150} = 0.0256$

The point elasticity of demand, E = 0.0256

• The demand is inelastic (less than 1) when the quantity demanded is 150 units

c. If the quantity demanded decreases from 150 to 140 units, we have;

$0.0256 \: = \frac{1}{13} \times \frac{p}{140} =$

Which gives;

p = 46.6

• The price when the quantity demanded decreases to 140 is $46.6

d. Given that increase in price, from 46.6 to 50, increases the quantity demanded from 140 to 150, therefore;

• The manufacturer should increase the price, p to increase the revenue, R.

R = p × q

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