Question

Amalgamated Popcorn, Inc. is a fairly small firm selling bags of flavored gourmet popcorn in a popular mall. As shop owner and operator, you have observed that your daily sales tend to follow a pattern that can be stated as:

QP = 500 - 100PP + 1.25A - 20PS + 2I

where QP = unit sales of popcorn bags, PP = price of bags in dollars, A = advertising expenses, PS = price of soda pop sold at your stand in dollars, I = per capita income of customers in thousands of dollars.
You are currently charging $1 per bag of popcorn, spending $200 in advertising, charging $1 for a soda pop, and per capita income is $22,000.
a. Compute the elasticity coefficients for price, income, and cross-price.
b. You are currently paying $.45 for popcorn (including cost for the corn, cost to pop, and bag) and currently charging $1 per bag of popcorn. Is this the profit-maximizing price? Explain.

Answer 1

The given equation is as follows -

Given -

PP = 1

A = 200

PS = 1

I = 22,000

a.)

Price Elasticity

Substituting values of A, PS and I in the given equation, we get -

Diffeerntiating with respect to Price

The formula of elasticity is given as -

We know that P = 1, and substituting value of PP in QP, we get QP = 44630

Hence we get elasticity as. -

Income Elasticity

Substituting values of A, PS and PP in the given equation, we get -

Diffeerntiating with respect to Income

The formula of elasticity is given as -

We know that I = 22,000 , and substituting value of I in QP, we get QP = 44630

Hence we get elasticity as. -

Cross - Price Elasticity

Substituting values of A, PP and I in the given equation, we get -

Diffeerntiating with respect to Price of Soda

The formula of elasticity is given as -

We know that PS = 1, and substituting value of PS in QP, we get QP = 44630

Hence we get elasticity as. -

​​​​​​​

b.)

NO, this is not profit maximising. We can assume that the condition is that of perfect competition. In perfect competition, it is not possible to make the kind of supernormal profit that this firm is making, since the marginal cost of production is only $.45 while the price is $1, which indicates a $.55 profit on every bag of popcorn sold. This is not the profit maximsing point, as the profit can be further increased by increasing the production to the point where the cost of production is equal to the price, that is the point where both the cost and the price are equal.