EXAM 2 SPRING 2022

OTM 732: Economics for Managers EXAM #2 THURSDSAY, APRIL 7, 2022 Printed Name: __________________________________ RULES: - Your answers on this exam will represent your work and only your work. - You may not use textbooks, materials from class, content online, assistance from others, or any other help on this exam. - You MAY use a calculator for arithmetic calculations. On my honor, I agree to abide by these rules. Signature: ______________________________________ There are 5 questions for a total of 100 points.

1) (25 points) You make delicious cupcakes that you mail to customers across the country. Your cupcakes are so unique and special that you have a great deal of pricing power. Your customers have identical demand curves for your cupcakes, and a representative customer’s demand curve is shown below. (It’s not needed, but the demand curve equation is P=5-0.2Q or Q=25-5P.) Suppose your MC=$1/cupcake, whether you produce lots or just a few cupcakes. To keep things simple, suppose there are no fixed costs, so FC=0. a) (9 points) Acting as a monopolist, show the standard pricing analysis on the graph below that identifies your profit-mamximing price and quantity for your representative customer. Shade areas representing your profit and CS. (PS and profit are the same here since FC=0). b) (8 points) Suppose you offer a quantity discount: first 10 cupcakes at $3 each and any cupcakes over 10 are offered at a discounted price. What discount price will maximize your profit? Show this quantity discount arrangement on your graph and shade areas representing your profit and CS.

2) (10 points) a) (4 points) A “menu” is a list of items for sale and their prices. Use the “menu” concept to explain the difference between second-degree price discrimination and third-degree price discrimination. b) (6 points) Provide a real-life example of second-degree price discrimination and explain why it is second-degree price discrimination. Provide a real-life example of third-degree price discrimination and explain why it is third-degree price discrimination. (Make sure that your explanations line up with your “menu” explanation in part (a).)

3) (20 points) Architectural Digest and the New Yorker magazines are both published by Conde Nast. The former did well in the 1990s, but the New Yorker struggled with sales. For these kinds of magazines, subscriptions and newsstand sales are important, but advertising revenue is even more important. Lower sales of the New Yorker meant that advertisers were less willing to advertise, leaving the New Yorker in a difficult financial position. This problem studies one response by Conde Nast: an advertising bundling strategy that started in January 1999. Suppose there are two types of advertisers who would consider placing ads these two magazines. Suppose also that there are equal numbers of each type of advertiser. The table below shows the willingness to pay for each type of advertiser for each magazine. Suppose that the marginal cost to Conde Nast of placing an ad is $100. a) If Conde Nast sells ads in these two magazines separately, what are the profit-maximizing prices for ads in the two magazines, what is the advertising profit for each magazine, and what is the overall advertising profit for Conde Nast? b) Conde Nast decided to bundle ads across the two magazines by requiring anyone who advertises in Architectural Digest to also advertise in the New Yorker . What is the profit- maximizing price for a bundle of ads in the two magazines? What is Conde Nast’s overall profit? $50 $250 New Yorker $800 $500 Architectural Digest Advertiser 2’s willingness to pay Advertiser 1’s willingness to pay

4) (20 points) Your internship company sells a medical device called MD1. Its marginal cost is MC 1 = 20. You have two potential customers: a clinic and a hospital. The clinic’s value for MD1 is 40 and the hospital’s value is 50. You cannot charge different customers different prices for the same product, so you have to quote the same price to the clinic and the hospital. a) (5 points) What price for MD1 maximizes your profit? Who buys at that price and what is your profit? Suppose that before you offer MD1 to the clinic and hospital, your company finalizes the development of MD2 that is both cheaper and higher quality than MD1. Specifically, it has MC 2 =15 and, because it is more effective than MD1, the clinic values it at 50 and the hospital values it at 80. Your internship supervisor is thrilled and tells you, “MD2 is cheaper and better, so we’re going to shut down MD1 operations, ramp up MD2 operations, and focus on selling MD2s to our customers!” b) (7 points) Suppose you shut down MD1 operations and ramp up MD2 operations. And suppose that MC 2 =15 and the MD2 values for the clinic and hospital are 50 and 80, respectively. Then what price for MD2 will maximize your profit? What is the resulting profit? Will your supervisor’s idea increase profit compared to the plan in part (a)?

After you do the analysis in part (b), you have an idea that you think might be better than your supervisor’s idea. You want to ramp up MD2 operations BUT continue offering MD1. Since MD1 and MD2 are different products, you can sell them at different prices, P 1 and P 2 . Of course, you know that if you offer prices P 1 and P 2 to one customer, then you must offer those same prices to your other customer. Finally, you know that each customer wants at most one device - an MD1 or an MD2 - and each will choose the device that offers them the greater consumer surplus (CS=Value-Price). c) (8 points) Can your idea generate more profit than your boss’s proposal in part (b)? If so, what P 1 and P 2 will maximize your firm’s profit? Who will buy MD1 and who will buy MD2? What profit does your idea generate? d) (0 points) Will you get a full-time offer or will your economic brilliance intimidate your supervisor?

EXAM 2 Formulas COST AND REVENUE DEFINITIONS TC = FC + TVC TR = PQ MC Q = TC Q – TC Q-1 MR Q = TR Q – TR Q-1 AC = TC/Q AR = TR/Q = P Profit: π = TR – TC. ELASTICITY If a factor F influences the demand Q for a product, the elasticity of demand for that product with respect to factor F is: . % % F Q E F    So the elasticity of demand for a good with respect to its price is: Price Elasticity = . % % P Q E P    With two data points, ) , ( 1 1 Q P and ) , ( 2 2 Q P , the ARC price elasticity between these points is: . )) ( 5 . 0 ( ) ( )) ( 5 . 0 ( ) ( / / % % 2 1 1 2 2 1 1 2 P P P P Q Q Q Q P P Q Q P Q E P            If E P < -1, demand is price elastic. If -1 < E P < 0, demand is price inelastic. PRICING A) Standard Pricing (one price for everyone, no two-part tariff, no price discrimination, no bundling, etc.) i) If the demand curve is 𝑃 = 𝑎 − 𝑏𝑄 (where 𝑎 and 𝑏 are some constants) then 𝑀𝑅 = 𝑎 − 2𝑏𝑄 . (Notice that the demand curve and 𝑀𝑅 have the same y-intercept and the slope of 𝑀𝑅 is twice the slope of the demand curve.) (Example: If 𝑃 = 100 − 2𝑄 , then 𝑀𝑅 = 100 − 4𝑄 .) Suppose the demand curve is written as 𝑄 = 𝑐 − 𝑑𝑃 (where 𝑐 and 𝑑 are some constants). Since this demand curve is in the form of Q as a function of P, we need to rewrite it in the form of P as a function of Q. We can do that with a little algebra and get 𝑃 = ௖ ௗ − ଵ ௗ 𝑄. Now we can apply our rule above to determine that 𝑀𝑅 = ௖ ௗ − ଶ ௗ 𝑄. (Notice the same y-intercept of ௖ ௗ and a slope that is twice as steep.) (Example: If 𝑄 = 100 − 5𝑃 , we can rewrite it as 𝑃 = 20 − 0.2𝑄 . Then 𝑀𝑅 = 20 − 0.4𝑄 .) ii) The profit-maximizing markup for a firm setting a single price for a single product is: ௉ିெ஼ ெ஼ = ିଵ ாାଵ . (Example: If 𝐸 =-3, then the optimal markup is ିଵ ିଷାଵ or ଵ ଶ , which means 50% markup. A couple variations on this equation are below. a) If you know 𝐸 and 𝑀𝐶 , the optimal price is: 𝑃 = ቂ ா ாାଵ ቃ 𝑀𝐶. (Example: If 𝐸 = −3 and 𝑀𝐶 = $50 /unit, the optimal price is 𝑃 = ቂ ିଷ ିଷାଵ ቃ 50 = $75 /unit.) b) A price 𝑃 is the profit-maximizing price if price elasticity solves: 𝐸 = ௉ ெ஼ି௉ . (Example: If 𝑀𝐶 = $50 /unit and we set 𝑃 = $75 /unit, then this price will maximize profit if 𝐸 = ଻ହ ହ଴ି଻ହ = −3. ) B) Two-Part Tariff Assuming a single demand curve, the profit-maximizing two-part tariff sets the price of a unit at 𝑃 = 𝑀𝐶 and sets the fee equal to the consumer surplus (CS) that results from that price.