Question

1. Understanding Elasticity
   1. Suppose that the elasticity of demand for apricots is – 2.3. If the grocery store raised price from $1.25 to $1.50 per pound, by how much would quantity change? Calculate what would happen to total revenues.

2. Suppose that when the price of gasoline was $3.00, the gas station sold 150,000 gallons per week. When the price of gasoline fell to $2.50, the gas station sold 175,000 gallons per week. Calculate the elasticity of demand and interpret.

3. When the price of peanut butter increased from $2.75 to $3.00, sales of jelly fell from 250 to 225. Calculate the cross-price elasticity and interpret.

Answer 1

a. Formula: Ed = %change in quantity/ %change in price

-2.3 = %change in quantity/ 20%

So, %change in quantity = -2.3 * 20% = -46%

When price increases from $1.25 to $1.50, quantity decreases by 46%

b. Formula: Ed = (∆Q/ ∆P) * P/Q, where,

∆Q = Q2-Q1;  ∆P = P2 - P1

Ed = (25,000/ - 0.50) * (3/ 150,000) = - 1

Price elasticity is -1. It is unitary elasticity.It means that when price fell, the quantity demanded increased proportionately.In other words, price fell by 16.67% and quantity demanded increased by 16.67%

c. Formula for cross elasticity of demand:

XED = ∆Qx/ Qx * Py/ ∆Py, where ∆Qx is Q2 - Q1 of jelly (or change in quantity of jelly); ∆Py = P2 - P1 of peanut butter (or change in price of peanut butter)

XED = (-25/ 250) * (2.75/ 0.25) = -1.1

Cross elasticity of demand between peanut butter and jelly is negative. A negative cross elasticity means that peanut butter and jelly are complements. When price of peanut butter increased, its demand fell, so did the demand for jelly. Price of peanut butter and quantity demanded of jelly move in opposite direction.