Question

Suppose the market demand for playing cards is given by the equation

Q = 6,000,000 – 1,000,000P where Q is the number of decks of cards demanded each year and P is the price in dollars. For a price increase from $2 to $3 per deck, what is the arc price elasticity?

Answer 1

Solution:

Arc price elasticity of demand =$\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price} ​$

Derive quantity demanded:

Quantity demanded at $2 = 6,000,000 – 1,000,000(2) = 6,000,000 – 2,000,000 = 4,000,000

Quantity demanded at $3 = 6,000,000 – 1,000,000(3) = 6,000,000 – 3,000,000 = 3,000,000

 

% change in qty demanded = $\frac{Q_{2} -Q_{1}}{(Q_{1}+Q_{2})/2 } \times 100$

$=\frac{3000000 -4000000}{(4000000+300000)/2 } \times 100 = \frac{-1000000}{3500000} \times 100 = -28.57\%$

% change in price =$=\frac{3 -2}{(2+3)/2 } \times 100 = \frac{1}{2.5} \times 100 = 40\%$

Arc price elasticity of demand =$=\frac{-28.57\%}{40\%} = -0.71$

Arc price elasticity of demand = 0.71

Therefore, it is price inelastic since it is below 1. That is a change in price causes a smaller percentage change in demand.