Question

Jessica Simpson sets up shop to sell “Buffalo Wings.” She observes that if the price drops from $3.50 per order to $2.50 per order, her daily sales rise from 300 to 500 orders. A. What is the price elasticity of demand for Jessica’s “Buffalo wings?” B. Which price yields the greater total revenue? C. Jessica is considering adding a new product, widgets, to the menu. She has experimented and discovered that a 10% increase in the price of wings causes a 20% increase in the quantity of widgets sold. What is the cross elasticity of demand between widgets and wings? Are they complements or substitutes?? D. What is the difference between the price elasticity of demand and the slope of the demand curve? Are they the same concept? Are they even related concepts?

Answer 1

(I) Price elasticity = 1/6

(II) the $2.5 price gives the higher revenue: 1,250

Step-by-step explanation:

(I) price elasticity

`E_s =((Q2 - Q1)/((Q2+Q1)/2))/((P2 - P1)/((P2+P1)/2))`

↑Q (500 - 300)/((500+ 300) / 2)

↑Q 200 / (800/2) = 200/400 = 1/2

↑P (3.5 - 2.5)/((3.5+2.5)/2)

↑P 1/(6/2) = 1/3

`Es = (1/2)/(1/3)  = 1/6`

(II) total revenue

3.5 x 300 = 1,050

2.5 x 500 = 1,250

Answer 2

A) the price elasticity of demand (PED) of Jessica's buffalo wings is:

PED = % change in quantity / % change in price

{Q2 - Q1 / [(Q2 + Q1) / 2]} / {P2 - P1 / [(P2 + P1) / 2]} = {500 - 300 / [(500 + 300) / 2]} / {3.50 - 2.50 / [(3.50 + 2.50) / 2]} = (200 / 400) / (1 / 3) = 0.5 / 0.33 = 1.52

B) $3.50 x 300 = $1,050

$2.50 x 500 = $1,250

A price of $2.50 per buffalo wing order will result in a total revenue of $1,250

C) Cross PED = % change in quantity demanded for Product A / % change in price of product B.

% change in quantity demanded of widgets / % change in price of wings = 20% / 10% = 2

Since the cross PED of widgets and wings is positive, then they are substitute products.

D) PED measures the proportional change in quantity demanded when the price of the product changes by 1%, while the slope of the demand curve measures the change in price due to a change in the quantity demanded.

Both concepts seem to be similar, their definitions include too many price changes and changes in the quantity demanded, but they measure different things. One measures a change in units and the other a change in price.