# Derive an expression for the inverse demand curve for Newton’s Donuts.

### 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**

**Location**

**Price**

80

55

65

70

80

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?