#### P7. 6 Optimal Input Mix.

The First National Bank received 3,000 inquiries following the latest advertisement describing its 30-month IRA accounts in the Boston World, a local newspaper. The most recent ad in a similar advertising campaign in Massachusetts Business, a regional business magazine, generated 1,000 inquiries. Each newspaper ad costs $500, whereas each magazine ad costs $125.

- A. Assuming that additional ads would generate similar response rates, is the bank running an optimal mix of newspaper and magazine ads? Why or why not? No, the bank is not running an optimal mix of newspaper and magazine ads because the optimal combination would occur when MPn / Pn = MPM / Pm? newspaper output: 3,000 / 500 = 6 and magazine output: 1,000 / 125 = 8. Therefore, the amount spent on newspaper ads attracted 6 inquiries while the amount spent on magazine ads attracted 8 inquiries. So to run an optimal mix of newspaper and magazine ads, the bank has to run more magazine ads and/ or fewer newspaper ads.
- B. Holding all else equal, how many inquiries must a newspaper ad attract for the current advertising mix to be optimal? For the current advertising mix to be optimal, MPn / Pn = MPM / Pm, therefore, to increase the newspaper output from 6 to 8.

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** Find:** MPn / 500 = 8 *500 ? mpn = 4,000 *500 So inquiries generated by newspaper ads would have to increase from 3,000 to 4,000. P7. 7

**Marginal Revenue Product of Labor.**

To better serve customers interested in buying cars over the Internet, Smart Motors, Inc., hired Nora Jones to respond to customer inquiries, offer price quotes, and write orders for leads generated by the company’s Web site. Last year, Jones averaged 1. 5 vehicle sales per week. On average, these vehicles sold for a retail price of $25,000 and brought the dealership a profit contribution of $1,000 each.

- A. Estimate Jones’ annual (50 workweeks) marginal revenue product. Jonas’ marginal revenue product can be found by the number of cars sold and the profit of each sale. MRPL = MPL * MRQ ? MRPL = (1. 5 * 50) * ($1,000) = $75,000 (Vehicles sales p/week * workweek) * (profit contribution).
- B. Jones earns a base salary of $60,000 per year, and Smart Motors pays an additional 28 percent of this base salary in taxes and various fringe benefits. Is Jones a profitable employee? oNo, Jones is not a profitable employee because her cost to be employed is $76,800 ($60,000 base salary + 28% of taxes and fringe benefits) and her marginal revenue product is only $75,000. Therefore, MRPL ($75,000) < PL ($76,800). This means that even though Jones brings in $75,000 additional profit it costs Smart Motors $76,800 to have her which means she brings $1,800 of marginal loss to Smart Motors.

** P7. 8 Optimal Input Level.**

Ticket Services, Inc., offers ticket promotion and handling services for concerts and sporting events. The Sherman Oaks, California, branch office makes heavy use of spot radio advertising on WHAM-AM, with each 30-second ad costing $100. During the past year, the following relation between advertising and ticket sales per **event has been observed:** Sales (units) = 5,000 + 100A - 0. 5A2?Sales (units) / ? Advertising = 100 - A Here, A represents a 30-second radio spot ad, and sales are measured in numbers of tickets. Rachel Green, manager for the Sherman Oaks office, has been asked to recommend an appropriate level of advertising. In thinking about this problem, Green noted its resemblance to the optimal resource employment problem studied in a managerial economics course. The advertising/sales relation could be thought of as a production function, with advertising as input and sales as the output. The problem is to determine the profit-maximizing level of employment for the input, advertising, in this “production” system. Green recognized that a measure of output value was needed to solve the problem. After reflection, Green determined that the value of output is $2 per ticket, the net marginal revenue earned by Ticket Services (price minus all marginal costs except advertising).

- A. Continuing with Green's production analogy, what is the marginal product of advertising? Marginal Product measures additional output from one more unit of the variable input. *APA = MS/MA = ? Sales (units) / ? Advertising (OR ? Q/? A) = 100 - A.
- B. What is the rule for determining the optimal amount of a resource to employ in a production system? Explain the logic underlying this rule. The rule for determining the optimal amount of a resource to employ is MRPA = PA (see slide 17) MPA * MRQ = PA (see slide 9). Does the above equation turn to: ?Q/? A *? TR/? Q =? TC/? A? Q’s cancel each other out and the equation turns to:?TR/? A =? TC/? This leads to Marginal Total Revenue (MTR) = Marginal Total Cost (MTC), which means the inflow = outflow.
- C. Using the rule for optimal resource employment, determine the profit-maximizing number of radio ads. oUsing the above equation MPA * MRQ = PA ? (100-A )* $2 = $100 $200-2A = $100 ? $100= 2A ? A=$50

** P7. 9 Net Marginal Revenue.**

Crane, Poole & Schmidt, LLC, is a successful Boston-based law firm. Worker productivity at the firm is measured in billable hours, which vary between partners and associates. Partner time is billed to clients at a rate of $250 per hour, whereas associate time is billed at a rate of $125 per hour. On average, each partner generates 25 billable hours per 40-hour workweek, with 15 hours spent on promotion, administrative, and supervisory responsibilities. Associates generate an average of 35 billable hours per 40-hour workweek and spend 5 hours per week in administrative and training meetings. Variable overhead costs an average of 50 percent of revenues generated by partners and 60 percent of revenues generated by associates.

- A. Calculate the annual (50 workweeks) net marginal revenue product of partners and associates.
**For Partners:**oMRPP = MPP * MRQ? MRPP = ($25 * 50) * ($250* 100% - 50%) = $156,250 (Billable hrs * workweek) * (rate billed * % overhead cost) For Associates: oMRPA = MPA * MRA ? MRPA = ($35 * 50) * ($125* 100% - 60%) = $87,500 (Billable hrs * workweek) * (rate billed * % overhead cost) Each marginal hour of effort by partner brings the firm $250 in revenue - $125 ($250 *50%) of variable costs, so a partner has a net marginal revue of $125 p/hr. ?Each marginal hour of effort by associate brings the firm $125 in revenue - $75($125 *60%) of variable costs, so a partner has a net marginal revue of $50 p/hr. Both of these reflect the marginal value of service output. - B. If partners earn $175,000 and associates earn $70,000 per year, does the company have an optimal combination of partners and associates? If not, why not? Make your answer explicit and support any recommendations for change. Comparing partners marginal revenue products with their salary shows MRPP = $156,250 ; $175,000. This means that partners bring $18,750 ($175,000-$156,250) marginal loss to the firm. comparing associates marginal revenue products with their salary shows MRPA = $87,500 ; $70,000. This means that associates bring $17,500 ($87,500-$70,000) marginal profit to the firm. Therefore to help move the company to an optimal combination where profit is maximized, they will have to either reduce the number of partners or have a small increase in the number of associates. This can be done by expanding the number of associates until MRPA = $70,000. After this is done we can recalculate the MRPP to see if it has increased. If the new MRPP = $175,000, no other change needs to be made.

**Chapter 7 PowerPoint Problem Stereo Receivers.**

Do-It-Yourself, Inc., sells budget-priced stereo receivers, in both kit and fully-assembled forms. Customers who assemble their own receivers benefit from the lower kit price of $100 per receiver. "Full-service" customers enjoy the luxury of an assembled receiver but pay a higher price of $150 per receiver. Both kit and fully assembled receiver prices are stable.

**The company has observed the following relation between the numbers of assembly workers employed per day and assembled receiver output:** Number of workers Finished receivers 00 18 214 318 420 521

- A. Construct a table showing the net marginal revenue product derived from assembly worker employment. Number of WorkersFinished receiversMarginal Product of Labor (MPL)Net Marginal Revenue Product of Labor (NMRPL) (1)(2)(3)(4) = (3) x $50 00N/AN/A 188$400 146$300 3184$200 4202$100 5211$50
- B. How many assemblers would Do-It-Yourself employ at a daily wage rate of $120? oDo-It-Yourself would employ 3 workers since from the table above, three workers NMRPL is $200 which is greater (;) than the $120 they would pay in wages.
- C. What is the highest daily wage rate Do-It-Yourself would pay to hire four assemblers per day? To hire four assemblers per day, the highest daily wage rate Do-It-Yourself should pay is $100 since that’s the NMRPL for the fourth worker.

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