Question

Peanut butter price went from $2 per pound to $4, while its quantity demanded dropped from 360 to 300 million pounds. Based on this information, please answer the following questions.

Question 14: What is the demand function for peanut butter? To answer this question, please solve for parameters a and b in P= a- bQ_D.

Question 15: Denote the elasticity of peanut butter demand with respect to price as E_DP. What is the value of E_DP at Q_D=360 million pounds? What about at QD=300 million pounds? And at the mid-point of Q_D=330 million pounds? Please use two methods to compute this last elasticity value.

Question 16: Is the peanut butter demand in this question elastic or inelastic to price?

Question 17: How would a price cut affect the total revenue from peanut butter sales? Explain your reasoning.

Answer 1

14. b = Change in P/Change in Q = (4-2)/(300-360) = -2/60 = -1/30
Absolute value of b = 1/30

At Qd = 300; P = 4
4 = a - (1/30)(300) = a - 10
So, a = 10+4 = 14

So, P = 14 - Q_D/30

15. dP/dQ = -1/20
So, dQ/dP = -30

At Q_D=360, E_DP = (dQ/dP)*(P/Q) = (-30)*(2/360) = -0.17

At Q_D=300, E_DP = (dQ/dP)*(P/Q) = (-30)*(4/300) = -0.4

Using mid point method,
E =

16. It is inelastic because absolute value of E_DP is less than 1.

17. A price cut would decrease total revenue from peanut butter sales because when demand is inelastic then a decraese in price will decrease revenue.