Answer to Question #198074 in Macroeconomics for hafsa

Question

4). Demand of a product is usually very sensitive to economic variables, such as the prices and consumer income. This responsiveness of demand is Compute elasticity in the below scenarios:

a). Yesterday, the price of envelopes was $3 a box, and Jacky was willing to buy 10 boxes. Today, the price has gone up to $3.75 a box, and Jacky is now willing to buy 8 boxes. Is Jacky’s demand for envelopes elastic or inelastic? What is Jacky’s elasticity of demand?

b). Katy advertises to sell cookies for $4 a dozen. She sells 50 dozen and decides that she can charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the 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

a)

To find Jacky's elasticity of demand, we need to divide the percent change in quantity by the percent change in price.

% Change in Quantity $= \dfrac{(8 - 10)}{(10)} = -0.20 =$ -20%

% Change in Price$= \dfrac{(3.75 - 3.00)}{(3.00)} = 0.25 =$ 25%

Elasticity $= |\dfrac{(-20)}{(25)}| = |-0.8| = 0.8$

His elasticity of demand is the absolute value of -0.8, or 0.8. Jacky's elasticity of demand is inelastic, since it is less than 1.

b)

To find Katy's elasticity of demand, we need to divide the percent change in quantity by the percent change in price.

% Change in Quantity $= \dfrac{(40 - 50)}{(50)} = -0.20 =$ -20%

% Change in Price $= \dfrac{(6.00 - 4.00)}{(4.00)} = 0.50$ = 50%

Elasticity = $|\dfrac{(-20)}{(50)}| = |-0.4| = 0.4$

The elasticity of demand is 0.4 (elastic).

To find the quantity when the price is $10 a box, we use the same formula:

Elasticity = 0.4 = |(% Change in Quantity)/(% Change in Price)|

% Change in Price =$\dfrac{(10.00 - 4.00)}{(4.00)} = 1.5 = 150$ %

Remember that before taking the absolute value, elasticity was -0.4, so use -0.4 to calculate the changes in quantity, or you will end up with a big increase in consumption, instead of a decrease!

-0.4 = |(% Change in Quantity)/(150%)|

|(%Change in Quantity)| = -60% = -0.6

$-0.6 = \dfrac{(X - 50)}{50}\\[9pt] X = 20$

The new demand at $10 a dozen will be 20 dozen cookies.