Question

2.Jamie’s Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, Jamie estimates the demand for flavored popcorn to be: Q = 1,200 − 800P + 2A, where A denotes advertising weekly spending (in dollars), Q is the bags of popcorn demanded and P is the price of a bag of popcorn. She is currently charging $1.50 per bag of popcorn (for which the marginal cost is $0.75) and spending $500 per week on advertising.

a) Compute and interpret the store’s price elasticity and advertising elasticity.

b) Check whether the current $1.50 price is profit maximizing. If not, determine the store’s optimal quantity and output. c) Examine if the store should consider increasing its spending on advertising.

Answer 1

Q = 1,200 - 800P +2A

Substitute the value of P and A

Q = 1,200 - 800(1.5) +2(500)

= 1,200 - 1200 + 1,000

= 1,000

a)

Price Elasticity = (dQ/dP)*P/Q

dq/dP= -800

substituting:

= - 800 *(1.5/1,000)

=1.2

Advertising elasticity:

Ea = dQ/dA *(A/Q)

dq/dA = 2

Ea = 2(500/1000)

= 1

b)

Q = 1,200 - 800P +2A

Substitute the value of A

Q = 1,200 - 800P+2(500)

= 1,200 - 800P + 1,000

Q= 2200 - 800P

800P = 2200 - Q

P = 2.75 - 0.00125Q

TR = . 2.75Q - 0.00125Q^2

MR = 2.75 - 0.0025Q

2.75 - 0.0025Q = 0

0.0025Q = 2.75

Q = 2.75/0.0025

= 1100

profit maximizing output is 1100.

c)

Advertisement elasticity is equal to unity. Hence, 10 % increase in advertisement would cause 10 % rise in sale. Firm can consider increasing its spending on adverisement.