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Calculate the price elasticity of demand for newtons donuts

**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.

Attribute Steak Restaurant Pizza Restautrant

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.

- 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.
- 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.
- 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.
- 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.

- Calculate the price elasticity of demand for Newton's Donuts and describe what it means. Describe your answer and show your calculations.
- Derive an expression for the inverse demand curve for Newton's Donuts. Describe your answer and show your calculations.
- 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)?
- Should Newton's Donuts spend more on advertising?

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