1. At Lou's Big City Parking Garage, Lou incurs marginal cost of $1 (MC=$1.00) per customer per hour. Because MC is constant, average variable cost (AVC) is equal to $1, as well, and because Lou engages in cost-plus pricing (i.e. prices for the long run), AVC is also equal to average total cost (AC). Assume each of Lou's customers has identical demand, given by the expression, P = 8.0 - 0.7Q, where Q is the number of hours of parking per customer, per day, and P is the price of parking per hour.
Assume, initially, Lou charges a single hourly price.
Use this information to answer the questions below.
a. With a single price, how much will Lou charge per hour to maximize profit, and how many hours will each customer per day?
b. With a single hourly price, what is Lou's markup and profit margin per customer?
c. With a single hourly price, what is Lou's profit per customer, per day? (2 pts.)
Suppose Lou is considering an alternative pricing scheme, in which he would charge $6 for the first three (3) hours of parking,
$3 for the next four hours of parking, and $1 per hour for the next three hours of parking (Note: After 10 hours, Lou would charge a fixed, daily rate).
In other words, Lou would engage in block pricing, a form of second-degree price discrimination.
d. Under this pricing scheme, and assuming each customer parks for the same number of hours as found above (in a.), what would be Lou's profit per customer, per day?
2. You are a manager in a large hotel chain that is about to open a hotel in a new city. You have been asked to determine the nightly rates that should be charged to the two distinct groups of customers that will stay at this hotel: tourists and business travelers. You can separate (and so identify) members of each group based on advanced booking. Therefore, you plan to implement third-degree price discrimination. To help you determine the profit-maximizing price for each group, you use a sample of data you have on these same groups of customers for the hotel chain in 50 other cities (these data can be found below). Based on prior research, you know that demand for both groups exhibit constant elasticity. Therefore, in using the data below, you will assume an exponential demand function, of the form: Q = APn, where Q is output (number of nightly stays per month), P is price per night, A is a constant, and "n" is the (constant) price elasticity of demand.
Part I: For each group of customers, run a regression to estimate "n," the price elasticity of demand for that group.
Part II: Use the results of your regressions to answer the question (determining the profit-maximizing price for each group).
a. Based on your regression results, enter a formula in the respective boxes below to calculate the profit-maximizing price for each group of customers.
3. You have just become the manager of a private golf club, and have been asked to come up with an annual membership (entry) fee as well as a price to charge for each round (18 holes) of golf. You have previously managed public golf courses and know from experience there are two types of golfers: "serious" and "occasional." In fact, you have annual survey data from your previous job in which you collected (for four years) data on the number of rounds each golfer played that year as well as whether the golfer had a subscription to the publication, "Golfer's Digest." A sample of the data can be found at the bottom of this problem, in which you have already divided the data into two equal groups, one consisting of 100 "serious" golfers (those with a subscription to "Golfer's Digest"), and the other group consisting of 100 "occasional" golfers (those without a subscription). Along with the annual number of rounds for each golfer, you also have the price of a round of golf corresponding to the year when the round was played.
Part I: For each group of 100 golfers, run a regression to estimate a simple demand equation (i.e. Q = a - bP), where Q (the dependent variable) represents the number of annual rounds of golf, P (the only explanatory variable) is the price per round, and "a" and "b" are the parameters to be estimated by the regression.
Part II: Use the results of your regressions to answer the questions below.
a. Based on your regression results, write the general expression for the respective demand equation
b. How much would the club charge for each round of golf?
c. Enter a formula to calculate the annual membership (entry) fee charged to each golfer.
d. You estimate there are 200 "serious" golfers at your new club. Enter a formula to calculate the club's profit from limiting membership to just this group of golfers.
e. How much would the club charge for each round of golf?
f. Enter a formula to calculate the annual membership (entry) fee charged to each golfer.
g. You project the club could attract 800 "occasional" golfers, in addition to the 200 "serious" golfers who are already members.
Enter a formula to calculate the club's profit in this case.
4. A company has two divisions. The first produces an operating system for mobile devices, such as smartphones. The other division manufacturers and markets its own smartphone. Of course, the company's smartphone runs on its own operating system (NOTE: Each smartphone contains one operating-system chip). Marginal cost of a chip in the operating-system division is $90, while marginal cost in the smartphone division--excluding the cost of the chip--is a constant $35 (thus, in this problem, AVC = MC). In addition, the price elasticity of demand for this company's smartphone is a constant -1.2 at every price level, with demand for the smartphone given by the function: Q = 56,375P-1.2., where P is the price per smartphone, and Q is the quantity of smartphones demanded, in millions.
For this entire problem, assume pricing is conducted over the long run (AC = AVC: all costs are variable).
In answering the questions below, you will consider two scenarios:
Part I: No external market for the operating system (the operating-system chips are strictly inputs to the company's smartphone division).
Part II: The operating system has its own external market, which is given by the inverse demand function: P = 145 - 1.5Q, where P is the price per chip, and Q is the quantity of chips (in millions).
Part I (No External Market for the Operating System):
a. What is the profit-maximizing price of a smartphone?
b. Enter the formula to calculate the profit-maximizing quantity of smartphones (in millions).
c. What is the company's profit (both divisions combined), in millions?
Part II (External Market for the Operating System):
a. Calculate the profit-maximizing quantity (in millions) and price of operating-system chips.
b. Enter a formula to calculate the profit (in millions) of the operating-system division.
c. Calculate the profit-maximizing price and quantity (in millions) of the company's smarthpones.
d. What is the company's overall profit (both divisions combined)--in millions?
e. Is the company buying or selling operating-system chips on the open market? Briefly explain.
Attachment:- Assignment.xlsx