Question

18. Consider the demand curve faced by a firm of P = 20 –

2q, where P is price and q is quantity

demanded. If the firm is currently charging P = 5, which statement is true?

a.

The firm is pricing where marginal revenue MR = 0

b.

The firm should increase price is t

hey wish to increase revenue.

c. The firm is selling its output in the elastic range of the demand curve

d.

The firm should decrease its price in order to increase revenue.

e.

A small change in price in either direction will result in zero change in total revenue

Answer 1

Answer

the elasticity of demand is:

$E=\frac{\partial q}{\partial p}*\frac{p}{q}\\ p=20-2q\\ 2q=20-p\\ q=10-0.5p\\ \frac{\partial q}{\partial p}=\frac{\partial \left ( 10-0.5p \right )}{\partial p}=-0.5\\ p=5\ and\ q=10-0.5*5=7.5\ units\\ E=-0.5*\frac{5}{7.5}=-\frac{1}{3}=-0.33$

The elasticity is 0.33 in absolute value which is less than 1 means the demand is inelastic

so option b is correct

The firm should increase its price if they wish to increase its revenue.

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MR=0 at E=1 but E=0.33 so option a is not correct

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demand is inelastic so the option c is not correct

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the revenue is maximum at unit elastic demand and decrease in price decreases elasticity in absolute terms so the revenue decreases at inelastic demand so option d is incorrect

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the small change in price will change the revenue as the demand is inelastic

the revenue does not change if the demand is unit elastic