Question

You are opening a pizzeria, and you have access to a secret survey of MSU students that reveals local pizza demand to be described by this function: Qp = 150 - 30Pp + 10Pj - 5GI, where Qp is the number of slices of pizza demanded, P_P is price of pizza, P_J is price of peanut butter and jelly sandwiches, and GI is the population of gluten intolerant individuals. For the 5 short-answer questions below, give answers in order with no dollar signs and decimal accuracy as indicated. Use negative signs if appropriate.

1) At Qp = 75 and Pp = 2.50, what is Total Revenue (in whole dollars, no dollar sign)?

2) At Qp = 75 and Pp = 2.50, what is own price elasticity of demand (2 decimal places)?

3) At Qp = 90 and Pp = 2.00, what is Total Revenue (in whole dollars, no dollar sign)?

4) At Qp = 90 and Pp = 2.00, what is own price elasticity of demand (2 decimal places)?

5) At what own-price elasticity do you expect total revenue to be highest for a linear demand function like this one (2 decimal places)?

Answer 1

Given: Qp = 150 - 30Pp + 10Pj - 5GI

1) Total revenue = TR = Qp * Pp

At Qp = 75 and Pp = 2.50

TR = 75 * 2.5 = 187.5 ~ 188

2) From demand equation,

dQp/dPp = -30

At Qp = 75 and Pp = 2.50,

Own price elasticity of demand = e = (Pp/Qp) * (dQp/dPp)

e = (2.5/75) * (-30) = -1

3) Total revenue = TR = Qp * Pp

At Qp = 90 and Pp = 2.00

TR = 90 * 2.00 = 180

4) From demand equation,

dQp/dPp = -30

At Qp = 90 and Pp = 2.00,

Own price elasticity of demand = e = (Pp/Qp) * (dQp/dPp)

e = (2/90) * (-30) = -0.67

5) When own price elasticity of demand is greater than 1, total revenue increases when price decreases. When own price elasticity of demand is less than 1, total revenue increases when price increases.  When own price elasticity of demand is equal to 1, total revenue does change with change in price.

The total revenue for a linear demand curve is highest when own price elasticity of demand is equal to one.

Thus, TR is maximum when Pp = 2.50 and Qp = 90 i.e. e = 1.