Question

Amalgamated Popcorn, Inc. sells bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, Rhea 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 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

When P = 1.5 and A = 500,

Q = 1,200 - 800 x 1.5 + 2 x 500 = 1,200 - 1,200 + 1,000 = 1,000

(a)

Price elasticity = ($\partial$Q/$\partial$P) x (P/Q) = - 800 x (1.5/1,000) = - 1.2

Advertising elasticity = ($\partial$Q/$\partial$A) x (A/Q) = 2 x (500/1,000) = 1

(b)

Q = 1,200 - 800P + 1,000 = 2,200 - 800P

P = (2,200 - Q)/800 = 2.75 - 0.00125Q

TR = PQ = 2.75Q - 0.00125Q²

MR = dTR/dQ = 2.75Q - 0.0025Q

Setting MR = MC,

2.75Q - 0.0025Q = 0.75

0.0025Q = 2

Q = 800

P = 2.75 - (0.00125 x 800) = 2.75 - 1 = $1.75

So, P = $1.5 is not profit-maximizing.

(c)

Since advertising elasticity > 0, sales will increase with increase in advertising and store should consider increasing its advertising.