Week 2 Assignment: Consumer Demand Analysis And Estimation

Week 2 Assignmentconsumer Demand Analysis And Estimation Applied Pro

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. The attributes are Taste, Location, and Price, with the following ratings:

• 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.

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.

Provide a description of a scenario in the “real-world” business setting where this decision-making approach applies. Discuss the benefits and drawbacks of 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; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values are Ax=120, Px=0.95, and Py=0.64.

Show all calculations and describe your answers for each question in complete sentences.

1. Calculate the price elasticity of demand for Newton’s Donuts and interpret its meaning. Show your calculations.
2. Derive an expression for the inverse demand curve for Newton’s Donuts. Show your calculations.
3. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price to sell more donuts (assuming profit maximization)? Should Newton’s Donuts spend more on advertising? Describe your reasoning.

Paper For Above instruction

In this analysis, we explore consumer demand estimation techniques applied to real-world business decisions, focusing on utility maximization and demand elasticity. The case of Patricia's restaurant venue selection illustrates how attribute-based utility models guide strategic decisions, while Newton’s Donuts case exemplifies demand function analysis for pricing and advertising strategies.

Part 1: Restaurant Venue Choice and Utility Analysis

Patricia's decision-making process involves evaluating two main locations—suburban and metropolitan Los Angeles—based on the attributes of taste, location, and price. She considers two restaurant types: steak and pizza. The utility associated with each option can be modeled using a weighted sum of attribute ratings, where weights reflect attribute importance based on location type.

Attribute importance weights

In a suburban setting, taste is three times as important as location and twice as important as price. Let the weight of taste be T, location be L, and price be P. Then:

• T = 3 * L
• T = 2 * P

Assuming the weights sum to 1 for normalization:

Set total weight: W = T + L + P. Substituting T in terms of L and P:

• T = 3L
• T = 2P

Express L and P in terms of T:

• L = T/3
• P = T/2

Sum of weights: T + T/3 + T/2 = 1

Calculating common denominator 6:

T(6/6) + T(2/6) + T*(3/6) = 1 → (6T + 2T + 3T)/6 = 1 → 11T/6 = 1 → T = 6/11 ≈ 0.545

Thus, L = T/3 ≈ 0.545/3 ≈ 0.182, P = T/2 ≈ 0.545/2 ≈ 0.273

The weights are approximately:

• Taste: 0.545
• Location: 0.182
• Price: 0.273

(Note: Since ratings are on a 1–100 scale, each attribute rating must be normalized accordingly, or ratings are directly multiplied by these weights.)

Evaluating Restaurant Options in Suburban Area

Suppose the ratings for each attribute are as follows:

• Steak Restaurant: Taste = 85, Location = 70, Price = 75
• Pizza Restaurant: Taste = 78, Location = 80, Price = 70

Calculating total utility:

Steak: U = 850.545 + 700.182 + 75*0.273 ≈ 46.33 + 12.74 + 20.48 ≈ 79.55

Pizza: U = 780.545 + 800.182 + 70*0.273 ≈ 42.51 + 14.56 + 19.11 ≈ 76.18

Patricia should pursue the steak restaurant in a suburban area due to the higher total utility score (79.55 vs. 76.18).

Evaluating Options in the Los Angeles Metropolitan Area

In this scenario, location becomes three times as important as taste and two times as important as price, reversing the weights. Calculations are similar but with different importance weights:

• L = 3*T
• P = (1/2)*T

W = T + 3T + (T/2) = 1. Using common denominator 2: T/2 + 3T/2 + T/2 = 1 → (T + 3T + T)/2 = 1 → (5T)/2 = 1 → T = 2/5 = 0.4

Then, L = 3*T = 1.2 (which exceeds 1, indicating that weights need normalization; normalization involves dividing all weights by sum of weights.)

Sum: T + L + P = 0.4 + 1.2 + 0.2 = 1.8. Normalized:

• Taste: 0.4 / 1.8 ≈ 0.222
• Location: 1.2 / 1.8 ≈ 0.667
• Price: 0.2 / 1.8 ≈ 0.111

Using the same attribute ratings as before, the total utility in the metro area becomes:

Steak: U = 850.222 + 700.667 + 75*0.111 ≈ 18.87 + 46.69 + 8.33 ≈ 73.89

Pizza: U = 780.222 + 800.667 + 70*0.111 ≈ 17.32 + 53.36 + 7.78 ≈ 78.46

In this case, Patricia should pursue the pizza restaurant due to higher utility (78.46 vs. 73.89).

Influence of Venue Probabilities

Considering the probabilities p_suburban=0.7 and p_metro=0.3, expected utility for each restaurant combines utilities with these probabilities:

Expected Utility (Steak) = 0.7 79.55 + 0.3 73.89 ≈ 55.69 + 22.17 ≈ 77.86

Expected Utility (Pizza) = 0.7 76.18 + 0.3 78.46 ≈ 53.33 + 23.54 ≈ 76.87

Patricia should pursue the steak restaurant based on higher expected utility (77.86 vs. 76.87). This probabilistic approach helps incorporate uncertainty in location availability into strategic decisions.

Real-World Scenario and Method Evaluation

This attribute-based utility model is applicable in various real-world business decisions, such as selecting suppliers, product design features, or market entry strategies. The benefit lies in quantitative comparison of options considering multiple attributes, enabling data-driven decisions. However, it relies heavily on accurate ratings and weight assignments, which may be subjective or difficult to estimate precisely, leading to potential biases or misjudgments.

Part 2: Demand Function Analysis for Newton’s Donuts

The demand function is given as: Qx = -14 – 54Px + 45Py + 0.62Ax. Substituting current values: Ax=120, Px=0.95, Py=0.64, we calculate:

Qx = -14 - 540.95 + 450.64 + 0.62*120

Qx = -14 - 51.3 + 28.8 + 74.4 ≈ -14 - 51.3 + 103.2 ≈ 37.9 (thousands of donuts)

Price Elasticity of Demand:

Elasticity (E) = (dQ/dP) * (P/Q). The derivative dQ/dP = -54 (coefficient of Px).

Using current Px=0.95 and Qx≈37.9, and P=0.95:

E = -54 (0.95 / 37.9) ≈ -54 0.025 ≈ -1.35

The magnitude of elasticity is 1.35, indicating demand is elastic. A 1% decrease in price would increase quantity demanded by approximately 1.35%, suggesting the company can increase sales through price reductions for profit gains.

Inverse Demand Curve:

Rearranged as Px = a function of Qx.

Starting from Qx = -14 – 54Px + 45Py + 0.62Ax:

54Px = -14 + 45Py + 0.62Ax - Qx

Px = (-14 + 45Py + 0.62Ax - Qx) / 54

Plugging in current values yields:

Px = (-14 + 28.8 + 74.4 - Qx) / 54 = (89.2 - Qx) / 54

Pricing and Advertising Decisions:

Given the elasticity and current profit margins (cost of $0.15 per donut), reducing the price from $0.95 may increase total profit if the increased quantity sold offsets the lower unit profit. Since demand is elastic (elasticity > 1 in magnitude), lowering price should increase total revenue and profit, assuming fixed costs are negligible or covered. Additionally, increased advertising spending (Ax=120) boosts demand; if marginal revenue from additional advertising exceeds its cost, increasing ad expenditure could be justified for long-term growth.

Conclusion

This analysis demonstrates how attribute-based utility models assist strategic restaurant location choices by quantifying consumer preferences, while demand function analysis guides pricing and advertising strategies for impulse products like donuts. Both models highlight the importance of data-driven decision-making in competitive markets.

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