1.A monopoly is considering selling several units of a homogeneous product as a single package. A typical consumer’s demand for the product is Qd = 130 - 0.25P, and the marginal cost of production is $160.
a. Determine the optimal number of units to put in a package.
__ units
b. How much should the firm charge for this package?
$ __
2.Suppose the European Union (EU) is investigating a proposed merger between two of the largest distillers of premium Scotch liquor. Based on some economists’ definition of the relevant market, the two firms proposing to merge enjoyed a combined market share of about two-thirds, while another firm essentially controlled the remaining share of the market. Additionally, suppose that the (wholesale) market elasticity of demand for Scotch liquor is -1.7 and that it costs $16.80 to produce and distribute each liter of Scotch.
Based only on these data, provide quantitative estimates of the likely pre- and postmerger prices in the wholesale market for premium Scotch liquor.
Instruction: Do not round intermediate calculations. Enter your final responses rounded to the nearest penny (two decimal places).
Pre-merger price: $ __
Post-merger price: $ __
3.The American Baker’s Association reports that annual sales of bakery goods last year rose 15 percent, driven by a 50 percent increase in the demand for bran muffins. Most of the increase was attributed to a report that diets rich in bran help prevent certain types of cancer. You are the manager of a bakery that produces and packages gourmet bran muffins, and you currently sell bran muffins in packages of three. However, as a result of this new report, a typical consumer’s inverse demand for your bran muffins is now P = 10 - 0.5Q.
If your cost of producing bran muffins is C(Q) = 5.5Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.
Instruction: Enter your response for the optimal package price rounded to two decimal places.
Optimal package size: _____units
Optimal package price: $ __
Sample Solution