Question

1. Assume that Bradley Corporation Inc. produces advanced analytic software for computer simulations called Market-It. Based on an analysis of product sales over a two-year period, Bradley’s marketing department estimates the demand for Market-It to be QM = 1,200 − 8PM + 4PS, where QM denotes units sold of Market-It software, PM denotes Market-It’s price, and PS denotes the price of a (competing) best-selling statistical software package (with both prices in dollars).

a) Currently, PM = $200 and PS = $300. What is the predicted demand for Market-It software?

b) The price PS has been unchanged at $300 during the last 6 months. Given this information, derive the equation for Market-It’s demand curve (with QM as the left-side variable). Also determine its inverse demand curve (with PM as the left-side variable).

c) An industry analyst comments that demand for Market-It is not very sensitive to changes in the price of the competing statistical software package PS. (This package does perform someof the same operations as Market-It, but not as quickly or conveniently.) Carefully assess this claim. Is his claim correct?

d) Suppose the marginal cost of producing Market-It is negligible. However, the company incurred signiﬁcant costs in developing the product for market (estimated to be about $350,000). Using Market-It’s estimated demand curve, determine the optimal price and output for Market-It.

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.

3. [Price Discrimination Application] You are the marketing manager of a ﬁrm that produces carbon ﬁber and sells this composite material to two distinct kinds of customers: satellite producers and bicycle manufacturers. Demand for carbon ﬁber by these two market segments is quite diﬀerent, as described by the respective price equations: PS = 10−QS/600 and PB = 12−QB/100, where annual quantities [QS and QB] are in thousands of pounds and prices [PS and PB] are in dollars. Your ﬁrm estimates the marginal cost of carbon ﬁber production at $4 per pound.

a) For each segment, determine the ﬁrm’s proﬁt-maximizing price and output. Is the ﬁrm practicing price discrimination?

b) Because of carbon
ﬁber shortages, the ﬁrm’s total production capacity drops to only
1.5 million pounds per year. Determine the ﬁrm’s optimal quantities
and prices in this case. (hint: you can use Solver in Excel to
solve this question, but you don’t need to)

Answer #1

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