Consumer Demand Analysis And Estimation Applied Probl 077773 ✓ Solved

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

• Taste
• Location
• Price

Pizza Restaurant

• Taste
• Location
• Price

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

a. 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.

b. 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.

c. 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.

d. 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.

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

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

c. 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)?

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

Paper For Above Instructions

Problem 1:

Patricia is evaluating two restaurant venues: a steak restaurant and a pizza restaurant, weighing three important attributes: taste, location, and price. The way she values these factors dramatically changes based on the location of her restaurant.

Suburban Area Analysis:

In a suburban setting, the importance of each attribute can be assigned the following weights based on the stated importance: Taste (6), Location (2), and Price (3). This gives a total weight (6 + 2 + 3 = 11).

Suppose the Steak Restaurant is rated as follows: Taste = 80, Location = 70, Price = 60. The total score for Steak can be calculated as:

Total Utility (Steak) = (Taste Score × Weight) + (Location Score × Weight) + (Price Score × Weight) = (80 × 6/11) + (70 × 2/11) + (60 × 3/11) = 47.27 + 12.73 + 16.36 ≈ 76.36.

Suppose the Pizza Restaurant is rated as follows: Taste = 75, Location = 65, Price = 57. The total utility for Pizza can be calculated as:

Total Utility (Pizza) = (75 × 6/11) + (65 × 2/11) + (57 × 3/11) = 40.91 + 11.82 + 15.55 ≈ 68.28.

Therefore, if Patricia wants to open a restaurant in a suburban area of Los Angeles, she should pursue the Steak Restaurant because it has a higher utility score of 76.36 compared to the Pizza Restaurant's 68.28.

Los Angeles Metropolitan Area Analysis:

In this case, the weight changes, reflecting the suburban area context. If opening in a metropolitan area, we swap the weights: Taste (1), Location (3), and Price (2), leading to a total weight of (1 + 3 + 2 = 6).

Utilizing the previous ratings:

Total Utility (Steak) = (80 × 1/6) + (70 × 3/6) + (60 × 2/6) = 13.33 + 35 + 20 = 68.33.

Total Utility (Pizza) = (75 × 1/6) + (65 × 3/6) + (57 × 2/6) = 12.5 + 32.5 + 19 = 64.

Consequently, Patricia should choose the Steak Restaurant for the metropolitan area as well since it yields a higher utility score of 68.33 as compared to Pizza's utility of 64.

Weighted Probability Analysis:

Considering the probabilities of suitable areas for the restaurant: suburban at 0.7 and metropolitan at 0.3, we calculate expected utility:

Expected Utility = P(suburban) × Utility(suburban) + P(metropolitan) × Utility(metropolitan).

For Steak: Expected Utility (Steak) = (0.7 × 76.36) + (0.3 × 68.33) ≈ 53.45 + 20.50 = 73.95.

For Pizza: Expected Utility (Pizza) = (0.7 × 68.28) + (0.3 × 64) ≈ 47.78 + 19.2 = 66.98.

Patricia should pursue the Steak Restaurant as the combined expected utility is greater than that of Pizza.

Real-World Application:

This decision-making process could apply to new product launches, where a company must weigh product features against market conditions and potential pricing strategies. Benefits include systematic analysis and decision justification, whereas drawbacks encompass potential oversimplification of complex decisions, assuming linearity in attributes.

Problem 2:

The demand function for Newton’s Donuts is given by Qx = -14 – 54Px + 45Py + 0.62Ax. Using the current values of Ax=120, Px=0.95, and Py=0.64, we substitute values for Qx:

Qx = -14 - 54(0.95) + 45(0.64) + 0.62(120) = -14 - 51.3 + 28.8 + 74.4 = 37.9 thousands of donuts.

Price Elasticity of Demand:

Price elasticity of demand (PED) is calculated using the derivative of the demand function with respect to price. PED = (dQ/dPx) * (Px/Qx). Thus, the derivative dQ/dPx = -54. Substituting in values,:

PED = (-54) * (0.95/37.9) ≈ -1.4, indicating demand is elastic, meaning that a 1% increase in price would lead to a percentage decrease of 1.4% in quantity demanded.

Inverse Demand Curve:

To derive the inverse demand curve, rearranging Qx = -14 - 54Px + 45Py + 0.62Ax for Px:

Px = (-14 + 45Py + 0.62Ax - Qx)/54. Substituting Ax=120 and Py=0.64 gives us an inverse demand function dependent on Qx.

Price Discussion:

If producing costs are $0.15, and current price is $0.95, the profit margin is high. A price reduction may increase sales dramatically, given the elasticity measures.

Advertising Decision:

Considering the elasticity of 0.62 implies a positive effect on demand per advertising dollar spent. It may rightfully suggest that increasing advertising spend could further boost the overall demand.

References

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