Problem 1) Qopy Qatt specializes in printing business cards and resume is, using the latest laser technology. After analysis of the business, the manager has determined that weekly demand can be approximated by Q=25,000 = 1000P. The firm’s cost function is C=25,000 + 13Q + 002Q^2, where Q is output per week.
A) Determine the profit maximizing price and output.
B) The night supervisor believes that extending Qopy Qatt’s hours by two hours in the evening would substantially increase volume. The manager is willing to stay open for two hours over the next three months as an experiment. What results would lead you to recommend that Qopy Qatt remain open later in the evening on a permanent basis?
C) A former employee decides to sue Qopy Qatt, alleging employment discrimination. Although management claims innocence, they agree to settle out of court. The settlement requires Qopy Qatt to pay the employee $10,000 per month for the next year. Determine the optimal price and output for the shop under these new conditions.
Problem 2) Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers' chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to be described by: C = $50,000 +0.25Q Night Timers' president seeks to establish a price that maximizes profit. She thinks that the firm should be able to sell at least 125,000 rolls of tape per year.
A) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only sell 100,000?
B) The marketing manager forecasts demand for the tape to be: Q = 350,000 - 200,000P. Find the firm’s profit-maximizing output and price.
C) If the demand forecast in part b is realized in the first year of production, should the company consider expanding capacity? Explain.
Problem 3) Nearby college has done a study of college enrollments and has concluded that the number of students in the fall term is Q=5000 - .5T + .1Y + .2Tc
Where Q = number of students enrolled full-time, T = tuition charged by Nearby, Y= national GDP in billions, and Tc = tuition charged by competition college, a school across town.
A) Determine enrollment if T = $14000, Y = $7500 billion and Tc = $16,000. Determine elasticity of demand for Nearby at this tuition rate.
B) The admissions office of Nearby proposes an advertising campaign, designed to convince potential students that it is an underrated educational bargain. The cost of the campaign is set at $4,500,000. Nearby’s admission office thinks that this will change demand to Q= 7500 = .4T + .15Y +. 2Tc. If the admission office is correct, how many students will enroll next fall? What is demand elasticity at the new enrollment? Is the advertising campaign cost effective?
Problem 4) War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 – 0.002 Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacture (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q.
A) If the goal of War Game is to maximize profit, calculate the optimal output and price.
B) If instead the company’s goal is to maximize sales revenue, what is its optimal price and quantity?
Problem 5) You are the marketing manager of a firm that ships specialty aluminum products from a mill to two different markets. You think that demand may be different in the markets and your consultant agrees. She has measured demand in the markets as Qa = 10,000 – 40Pa and Qb = 8,000 – 60 Pb Where Qa = quantity in market A, Qb = quantity market B and P is the price changed.
Assume that marginal cost of production is $75 per unit.
A) Suppose you do not price discriminate. What is the optimal price and quantity for the markets? What is your total revenue? (Hint: Pa = Pb)
B) If your goal is maximize profit, determine optimal prices to charge in the markets. Compute your new revenue.
Problem 6) Gold Trackers monitors the price of precious metals, and has daily data on prices and sales of gold for the past several years. One of their new MBA financial wizards has estimated the following relationship for gold sales in the past year of trading (250 observations).
Q= 4,000 – 0.01P + 1.5I – 1.25X + 2.0S R^2 = .96
(857) (0.002) (0.65) (0.44) (0.48)
Where Q = daily sale of gold in ounces, P is the price of gold in dollars per ounce, I is the most recent one month report on U.S. CPI Inflation (in %), X is an index of the exchange rate of the U.S. dollar compared to seven other currencies, and S is the market price of an ounce of silver in dollars. Standard errors are in parenthesis.
A) Evaluate the results of the this regression
B) Recently, the price of gold has been $380 per ounce, inflation was measured at 0.2% for the month, the dollar has been trading at 99.7 on the foreign exchange index, and silver has been steady at $4.75 per ounce. What is the expected quantity of gold that will trade on a daily basis?
C) Are gold and silver substitutes or complements? Explain
Problem 7: A firm faces the demand curve, P= 80 -3Q, and has the cost equation C= 200 + 20Q.
A) Find the optimal quantity and price for the firm.
B) Now suppose that demand changes to P = 110 – 3Q. Find the new optimal price and quantity. Has there been an increase or a decrease in demand? Explain.
Problem 8) Suppose that a firm sells in a competitive market at a fixed price of $12 per unit. The firm’s cost function is C = 200 + 4Q. Determine the minimum quantity at which the firm can break even. Are there multiple break-even points? Explain in detail.