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**Consumer Demand Analysis and Estimation Applied Problems**

Please complete the following two applied problems:

** Problem 1:** Patricia is researching venues for a restaurant business. She is evaluating three major attributes that she considers important in her choice: taste, location, and price. The value she places on each attribute, however, differs according to what type of restaurant she is going to start. If she opens a restaurant in a suburban area of Los Angeles, then taste is the most important attribute, three times as important as location, and two times as important as price. If she opens a restaurant in the Los Angeles metropolitan area, then location becomes three times as important as taste and two times as important as price. She is considering two venues, respectively, a steak restaurant and a pizza restaurant, both of which are priced the same. She has rated each attribute on a scale of 1 to 100 for each of the two different types of restaurants.

** Steak Restaurant Pizza Restaurant**

**Taste 80 70**

**Location 55 80**

**Price 65 50**

Show all of your calculations and processes. Describe your answer for each question in complete sentences.

1. Which of the two options should Patricia pursue if she wants to open a restaurant in a suburban area of Los Angeles? Calculate the total expected utility from each restaurant option and compare. Graph is not required. Describe your answer, and show your calculations.

2. Which of the two options should she pick if she plans to open a restaurant in the Los Angeles metropolitan area? Describe your answer, and show your calculations.

3. Which option should she pursue if the probability of finding a restaurant venue in a suburban area can be reliably estimated as 0.7 and in a metropolitan area as 0.3? Describe your reasoning and show your calculations.

4. Provide a description of a scenario in which this kind of decision between two choices, based on weighing their underlying attributes, applies in the “real-world” business setting. Furthermore, what are the benefits and drawbacks, if any, to this method of decision making?

** Problem 2:** The demand function for Newton’s Donuts has been estimated as follows:Qx = -14 – 54Px + 45Py + 0.62Ax where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

1. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations.

2. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations.

3. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company’s goal)?

4. Should Newton’s Donuts spend more on advertising?

**Problem 3:** Production Cost Analysis and Estimation

William is the owner of a small pizza shop and is thinking of increasing products and lowering costs. William’s pizza shop owns four ovens and the cost of the four ovens is $1,000. Each worker is paid $500 per week.

workers employed

Qty of pizzas produced per week

0

0

1

75

2

180

3

360

4

600

5

900

6

1140

7

1260

8

1360

**Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.**

**Which inputs are fixed and which are variable in the production function of William’s pizza shop? Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed?**

**What number of workers appears to be most efficient in terms of pizza product per worker?**

**How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer.**

** Problem 4:** Production Cost Analysis and Estimation

**Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.**

**Describe and derive an expression for the marginal cost (MC) curve.**

**Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes).**

**What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output.**

**Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation.**

**Problem 5: **Price Quotes and Pricing Decisions

**1. Your company, Bright Paints, is one of a dozen companies manufacturing a special reflective paint used for traffic signs. The State Department of Transportation has called for tenders to supply 10,000 gallons of blue reflective paint to be delivered within two months. You can foresee fitting in a production run of the blue paint and have decided to bid on the job. You calculate your incremental costs for this job to be $76,200. This particular contract is standard, similar in all in respects to hundreds of contracts you have bid on over the past few years. Your pricing policy has been to apply a mark-up to incremental costs to arrive at the bid price. Your mark-up has been higher when you had plenty of orders and lower when you had few or no orders to fulfill. You have assembled data relating the mark-up rate used and the percentage of contracts won at each mark-up rate, as follows.**

**Mark-up rate (%)**

**Percentage of contracts won at that rate (%)**

**0**

**10**

**15**

**20**

**25**

**30**

**35**

**95.9**

**84.8**

**65.4**

**41.3**

**15.7**

**3.0**

**0.**

**a. ****Why would your company have bid with a zero mark-up on some past tenders? Why didn’t it win all of those contracts?**

**b. ****What is the bid price that maximizes the expected contribution of the contract?**

**c. ****Why, or why not, is the fixed-price mode of bidding likely to be the best one to use for this contract?**

**Problem 6: **Price Quotes and Pricing Decisions

**In calculating the incremental cost of a particular project, how would you treat the possible future costs of a lawsuit that may occur as a result of this project, where the cost of the lawsuit might range from $10,000 to $500,000 with an associated probability distribution**

** Problem 7: **Market Structures and Pricing Decisions.Robert’s New Way Vacuum Cleaner Company is a newly started small business that produces vacuum cleaners and belongs to a monopolistically competitive market. Its demand curve for the product is expressed as Q = 5000 – 25P where Q is the number of vacuum cleaners per year and P is in dollars. Cost estimation processes have determined that the firm’s cost function is represented by TC = 1500 + 20Q + 0.02Q2.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

What are the profit-maximizing price and output levels? Explain them and calculate algebraically for equilibrium P (price) and Q (output). Then, plot the MC (marginal cost), D (demand), and MR (marginal revenue) curves graphically and illustrate the equilibrium point.

**How much economic profit do you expect that Robert’s company will make in the first year?**

**Do you expect this economic profit level to continue in subsequent years? Why or why not?**

**8: Market Structures and Pricing Decisions.**

**Greener Grass Company (GGC) competes with its main rival, Better Lawns and Gardens (BLG), in the supply and installation of in-ground lawn watering systems in the wealthy western suburbs of a major east-coast city. Last year, GGC’s price for the typical lawn system was $1,900 compared with BLG’s price of $2,100. GGC installed 9,960 systems, or about 60% of total sales and BLG installed the rest. (No doubt many additional systems were installed by do-it-yourself homeowners because the parts are readily available at hardware stores.)**

**GGC has substantial excess capacity–it could easily install 25,000 systems annually, as it has all the necessary equipment and can easily hire and train installers. Accordingly, GGC is considering expansion into the eastern suburbs, where the homeowners are less wealthy. In past years, both GGC and BLG have installed several hundred systems in the eastern suburbs but generally their sales efforts are met with the response that the systems are too expensive. GGC has hired you to recommend a pricing strategy for both the western and eastern suburb markets for this coming season. You have estimated two distinct demand functions, as follows:**

**Qw =2100 – 6.25Pgw + 3Pbw + 2100Ag – 1500Ab + 0.2Yw**

**for the western market and**

**Qe = 36620 – 25Pge + 7Pbe + 1180Ag – 950Ab + 0.085Ye**

**for the eastern market, where Q refers to the number of units sold; P refers to price level; A refers to advertising budgets of the firms (in millions); Y refers to average disposable income levels of the potential customers; the subscripts w and e refer to the western and eastern markets, respectively; and the subscripts g and b refer to GGC and BLG, respectively. GGC expects to spend $1.5 million (use Ag = 1.5) on advertising this coming year and expects BLG to spend $1.2 million (use Ab = 1.2) on advertising. The average household disposable income is $60,000 in the western suburbs and $30,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year because it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs, and its TV commercial has already been produced. GGC’s cost structure has been estimated as TVC = 750Q + 0.005Q2, where Q represents single lawn watering systems.**

**Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.**

**Derive the demand curves for GGC’s product in each market.**

**Derive GGC’s marginal revenue (MR) and marginal cost (MC) curves in each market. Show graphically GGC’s demand, MR, and MC curves for each market.**

**Derive algebraically the quantities that should be produced and sold, and the prices that should be charged, in each market.**

**Calculate the price elasticities of demand in each market and discuss these in relation to the prices to be charged in each market.**

**Add a short note to GGC management outlining any reservations and qualifications you may have concerning your price recommendations.**

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