Consumer Demand Analysis And Estimation Applied Problems ✓ Solved

Consumer Demand Analysis And Estimation Applied Problems

Consumer Demand Analysis And Estimation Applied Problems

Complete the following two applied problems:

Problem 1

Patricia is researching venues for a restaurant business. She is evaluating three major attributes: taste, location, and price. The value she places on each attribute differs based on the type of restaurant she opens. If she opens a restaurant in a suburban area of Los Angeles, 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, location becomes three times as important as taste and two times as important as price.

She is considering two venues, a steak restaurant and a pizza restaurant, both priced the same. She has rated each attribute on a scale of 1 to 100 for each type of restaurant. Calculate the total expected utility from each restaurant option and compare. Describe your answers for each question in complete sentences:

  1. Which option should Patricia pursue for the suburban area?
  2. What about in the metropolitan area?
  3. If the probability of finding a restaurant venue in a suburban area is 0.7 and in a metropolitan area is 0.3, which option should she pursue?
  4. Provide a real-world scenario where this kind of decision applies and discuss its benefits and drawbacks.

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. Show all calculations and processes:

  1. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means.
  2. Derive an expression for the inverse demand curve for Newton’s Donuts.
  3. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and sell more donuts?
  4. Should Newton’s Donuts spend more on advertising?

Paper For Above Instructions

In addressing Problem 1, we first need to calculate the expected utility for Patricia's two possible restaurant ventures: a steak restaurant and a pizza restaurant, considering the attributes of taste, location, and price.

Problem 1 Analysis

Suburban Area Analysis

In the suburban context, we can denote the importance figures for each attribute as:

  • Taste = 3 units
  • Location = 1 unit
  • Price = 1.5 units

Suppose both restaurants are rated as follows:

  • Steak Restaurant: Taste = 90, Location = 60, Price = 70
  • Pizza Restaurant: Taste = 80, Location = 50, Price = 70

Next, we calculate the total expected utility for both restaurant options:

Total Utility for Steak Restaurant:

Utility = (Taste 3) + (Location 1) + (Price 1.5) = (90 3) + (60 1) + (70 1.5) = 270 + 60 + 105 = 435

Total Utility for Pizza Restaurant:

Utility = (80 3) + (50 1) + (70 * 1.5) = (240) + (50) + (105) = 395

Based on the calculations, Patricia should pursue the Steak Restaurant in the suburban area, as it yields a higher expected utility of 435 compared to 395 for the Pizza Restaurant.

Metropolitan Area Analysis

In the metropolitan context, the importance shifts:

  • Taste = 1 unit
  • Location = 3 units
  • Price = 1.5 units

We will use the same ratings:

  • Steak Restaurant: Taste = 90, Location = 60, Price = 70
  • Pizza Restaurant: Taste = 80, Location = 50, Price = 70

Total Utility for Steak Restaurant in Metropolitan Area:

Utility = (Taste 1) + (Location 3) + (Price 1.5) = (90 1) + (60 3) + (70 1.5) = 360

Total Utility for Pizza Restaurant in Metropolitan Area:

Utility = (80 1) + (50 3) + (70 * 1.5) = (80) + (150) + (105) = 335

In this case as well, the Steak Restaurant has a higher utility (360) compared to the Pizza Restaurant (335), so Patricia should still choose the Steak Restaurant.

Weighted Probability Analysis

Using the estimated probabilities:

  • Suburban probability = 0.7
  • Metropolitan probability = 0.3

Weighted Utility Calculation:

Expected Utility for Steak = (Utility in Suburban Probability of Suburban) + (Utility in Metropolitan Probability of Metropolitan) = (435 0.7) + (360 0.3) = 304.5 + 108 = 412.5

Expected Utility for Pizza = (Utility in Suburban Probability of Suburban) + (Utility in Metropolitan Probability of Metropolitan) = (395 0.7) + (335 0.3) = 276.5 + 100.5 = 377

Thus, considering probabilities, Patricia should choose the Steak Restaurant as it has a higher expected utility of 412.5 compared to 377 for the Pizza Restaurant.

Real-World Scenario

This decision-making method can be applied in many scenarios such as selecting a new product line for a company, where attributes like cost, market demand, and profitability are weighed. The benefits include a structured approach to decision-making that quantifies potential outcomes, aiding in rational choices. However, drawbacks include the oversimplification of complex human preferences and the potential missed nuances in consumer behavior.

Problem 2 Analysis

Moving to Problem 2, we explore the demand function for Newton's Donuts, formulated as:

Qx = -14 – 54Px + 45Py + 0.62Ax

Using the variable values: Ax = 120, Px = 0.95, and Py = 0.64, we can determine the current demand:

Substituting, Qx = -14 - 54(0.95) + 45(0.64) + 0.62(120)

Calculating:

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

Price Elasticity of Demand

The formula for price elasticity of demand (E) is:

E = (dQx/dPx) * (Px/Qx)

From the demand function: dQx/dPx = -54.

Calculating E = -54 * (0.95/37.9) = -1.4.

This indicates that the demand for Newton's Donuts is elastic; a 1% increase in price would decrease quantity demanded by approximately 1.4%.

Inverse Demand Curve Derivation

To derive the inverse demand curve, rearranging gives us:

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

Price Reduction Analysis

To analyze whether the firm should reduce price, we use the profit maximization rule. If Px > MC, reducing the price to increase sales might be feasible. With a constant production cost of $0.15, the firm should evaluate max profit scenarios considering fixed vs variable costs.

Advertising Expenditure Assessment

To determine if they should spend more on advertising, we assess the marginal return on advertising. If increasing Ax increases Qx sufficiently to cover the advertising cost, then it is advisable to increase advertising efforts.

References

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