Question

if sam the pizzaiolo lowers the price of their pizzas from $6 to $5 and finds that sales increase from 400 to 600 pizzas per week, then the demand for sams pizzas in this range is:
a. inelastic.
b. unit elastic.
c. inferior.
d. elastic.

Explanation:

Step1: Define elasticity formula

Price elasticity of demand:
$$E_d = \frac{\% \Delta Q_d}{\% \Delta P}$$
Using midpoint method:
$$\% \Delta Q_d = \frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}} \times 100$$
$$\% \Delta P = \frac{P_2 - P_1}{\frac{P_2 + P_1}{2}} \times 100$$

Step2: Calculate % change in quantity

$Q_1=400$, $Q_2=600$
$$\% \Delta Q_d = \frac{600 - 400}{\frac{600 + 400}{2}} \times 100 = \frac{200}{500} \times 100 = 40\%$$

Step3: Calculate % change in price

$P_1=\$6$, $P_2=\$5$
$$\% \Delta P = \frac{5 - 6}{\frac{5 + 6}{2}} \times 100 = \frac{-1}{5.5} \times 100 \approx -18.18\%$$

Step4: Compute elasticity value

$$E_d = \frac{40\%}{-18.18\%} \approx -2.2$$
We use absolute value $|E_d| \approx 2.2$

Step5: Classify elasticity

Since $|E_d| > 1$, demand is elastic.

Answer:

d. elastic.