Answer to Question #235541 in Microeconomics for Johdrick

Question

Suppose the demand equation for cheese is

QD = 50 – 0.55P

Determine the price elasticity of demand when the price of cheese is

$6.00

$8.00

$10.00

$12.00

Identify whether demand is elastic, inelastic, or unit elastic at each price level.

Answer 1

(a) Let's find the quantity of the product if price is $6.00:

$$Q_d=50-0.55\cdot6=46.7.$$

Let's also write the inverse demand function:

$$P=90.9-1.81Q_d.$$

We can find the price elasticity of demand when the price of cheese is $6.00 as follows:

$$E_d=\dfrac{-1}{slope}\cdot\dfrac{P}{Q_d},$$ $$E_d=\dfrac{-1}{-1.81}\cdot\dfrac{6}{46.7}=0.07.$$

Since $E_d<1$, the price elasticity of demand is inelastic at this price level.

(b) Let's find the quantity of the product if price is $8.00:

$$Q_d=50-0.55\cdot8=45.6.$$

Then, we can find the price elasticity of demand when the price of cheese is $8.00 as follows:

$$E_d=\dfrac{-1}{-1.81}\cdot\dfrac{8}{45.6}=0.09.$$

Since $E_d<1$, the price elasticity of demand is inelastic at this price level.

(c) Let's find the quantity of the product if price is $10.00:

$$Q_d=50-0.55\cdot10=44.5.$$

Then, we can find the price elasticity of demand when the price of cheese is $10.00 as follows:

$$E_d=\dfrac{-1}{-1.81}\cdot\dfrac{10}{44.5}=0.12.$$

Since $E_d<1$, the price elasticity of demand is inelastic at this price level.

(d) Let's find the quantity of the product if price is $12.00:

$$Q_d=50-0.55\cdot12=43.4.$$

Then, we can find the price elasticity of demand when the price of cheese is $12.00 as follows:

$$E_d=\dfrac{-1}{-1.81}\cdot\dfrac{12}{43.4}=0.15.$$

Since $E_d<1$, the price elasticity of demand is inelastic at this price level.