Week 7 SCORM
A local video store estimates their average customer's demand per year is Q=7-2P, and knows the marginal cost of each rental is $0.5. How much should the store charge for an annual membership in order to extract all the consumer surplus via an optimal two-part pricing strategy? a. $9 b. $10 c. $11 d. $12
a. $9 Annual membership (consumer surplus taken) is the triangle part of willingness-to-pay 1) Graph inverse demand P=3.5-.5Qd to see P=3.5 as y-axis intercept; flat .5 MC 2) Solve for ideal quantity by setting P=MC 3.5-.5Qd=.5 -> Qd=6 ideal 3) Calculate triangle: .5 x b x h = .5 x 6 x (3.5-5) = $9
Suppose two types of consumers buy suits. Consumers of type A will pay $100 for a coat, and $50 for pants. Consumers of type B will pay $75 for a coat, and $75 for pants. The firm selling suits faces no competition and has a marginal cost of zero. The optimal commodity bundling strategy is: a. Charge $150 for a suit. b. Charge $75 for a suit. c. Charge $100 for a suit. d. Charge $125 for a suit.
a. Charge $150 for a suit. 1) Answer: charge $150 per suit bundle 2) Create relevant table of information so can find each consumer's bundle willingness to pay 3) Focus on bundle price: what is the highest value that both/all consumers share? Pricing at or below this will mean consumers' willingness-to-pay prompts them to buy the bundle 4) Calculate total revenue from bundle vs. total revenue if each item priced separately. For separate item pricing, if set lowest willingness-to-pay across consumers, all will buy that item. If price coats at $75, both A and B buy the coat.
A monopoly producing a chip at a marginal cost of $6 per unit faces a demand elasticity of -2.5. Which price should it charge to optimize it profits? a. $6 per unit b. $8 per unit c. $10 per unit d. $12 per unit
c. $10 per unit 1. Sub in numbers: P=6x[-2.5/(1-2.5)] 2. Simplify: P=6x(5/3)=$10 Check: Lerner index is (P-MC)/P ; here MC =$6, P=$10 L=(10-6)/10=0.40 : 40% of the final price is the mark-up component Mark-up factor: [1/(1-L)] = [1/(1-.4)] = 1.67 P=1.67x$6 MC = $10
You are the manager of a gas station and your goal is to maximize profits. Based on your past experience, the elasticity of demand by Texans for a carwash is -4, while the elasticity of demand by non-Texans for a car wash is -6. If you charge Texans $20 for a car wash, how much should you charge a man with Oklahoma license plates for a car wash? a. $1.50 b. $15 c. $18 d. $20
c. $18 Steps (Texans Ed=-4; non-Texans=-6). Price Texans=$20 1. Try to find underlying marginal cost overall using Texan data: 20=MCx[(-4)/(1-4)] -> 20x(3/4) = MC so MC = $15 2. Use the marginal cost =$15 and formula to find price to non-Texans (i.e. Oklahoma residents): P=15x[(-6)/(1-6)] = $18 3. Check theory: non-Texans have more elastic demand, so they should pay a lower price than Texans
The market inverse demand function for a good is P=6-2Q. Each consumer buys 1 unit, with the wealthiest consumers buying first. How much should the second wealthiest person be charged? a. $4 b. $6 c. $2 d. $1
c. $2 P=6-2Q inverse demand -1st wealthiest buyer Q=1 charged $4 -2nd wealthiest buyer Q=2 charged $2 -Unlikely 3rd buyer involved
What price should a firm charge for a package of two shirts given a marginal cost of $2 and an inverse demand function P = 6 - 2Q by the representative consumer? a. $2 b. $6 c. $8 d. $10
c. $8 Steps: P=6.2Q MC=$2 set Q=2 1. Solve for willingness-to-pay as $2 for last 2nd unit. 2. Graph: Find total willingness-to-pay as area under demand curve at that point: triangle + rectangle 3. Triangle intercept of $6 so height as ($6-$2); .5 x b x h=.5 x 2 x 4=$4 4. Total willingness-to-pay = $4+$4=$8; price to charge
