Answer to Question #175462 in Microeconomics for satti

Question

Q5. Katherine advertise to sell cookies for $4 a dozen. She sells 50 dozens and decided that she can charge more. She raise the price to $6 a dozen and sell 40 dozen. What is elasticity of demand? Assuming that the elasticity of demand is constant. How many would she sell if the price were $10 a box?

Answer 1

1 dozen = $4

50 dozens = $4$×$ 50 = $200

at the price of $6 per dozen,

40 dozens = $6$×$ 40 = $240

$Q_{o}=$ old quantity(50); $Q_{n}=$ new quantity(40); $P_{o}=$ old price(200); $P_{n}=$ new price(240)

$\epsilon=\frac{\frac{Q_{n}-Q_{o}}{Q_{o}}×100}{\frac{P_{n}-P_{o}}{P_{o}}×100}$

$\epsilon=\frac{\frac{40-50}{50}×100}{\frac{240-200}{200}×100}$

$\epsilon=$ 1 (elasticity is unitary)

if elasticity is constant, i.e. $\epsilon=1$, then the new quantity to be sold at $10 a box will be $x$ and the new price, $10x$

assume that

$\frac{\frac{Q_{n}-Q_{o}}{Q_{o}}×100}{\frac{P_{n}-P_{o}}{P_{o}}×100}=1$

$\frac{\frac{40-x}{40}×100}{\frac{240-10x}{240}×100}=1$

$x$ , (quantity to be sold at price $10 per box) is 22.2 dozens