Consumer Demand Analysis And Estimation Applied Probl 320079

Consumer Demand Analysis And Estimation Applied Problems

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.

Problem 1: Restaurant Venue Choice Analysis

Part A: Calculation of Attribute Weights for Suburban Area

In a suburban Los Angeles setting, taste (T) is the most important, with weights assigned based on the given ratios. Taste is set as the baseline with a weight of 1. Location (L) is three times as important as taste, so L = 3T = 3(1) = 3. Price (P) is half as important as taste, so P = T/2 = 0.5. To normalize these weights for comparison, we sum them: total weight = T + L + P = 1 + 3 + 0.5 = 4.5. The normalized weights are then:

• Taste: 1 / 4.5 ≈ 0.222
• Location: 3 / 4.5 ≈ 0.667
• Price: 0.5 / 4.5 ≈ 0.111

Part B: Calculating Utility for Suburban Area

Suppose Patricia's ratings for attributes are as follows:

• Steak Restaurant: Taste = 85, Location = 70, Price = 60
• Pizza Restaurant: Taste = 90, Location = 65, Price = 55

The total utility for each restaurant is calculated by multiplying each attribute rating by its weight and summing the results:

Utility = (Taste rating × weight) + (Location rating × weight) + (Price rating × weight)

For the steak restaurant:

Utility = (85×0.222) + (70×0.667) + (60×0.111) ≈ 18.87 + 46.69 + 6.67 ≈ 72.23

For the pizza restaurant:

Utility = (90×0.222) + (65×0.667) + (55×0.111) ≈ 19.98 + 43.36 + 6.11 ≈ 69.45

Since the steak restaurant yields higher utility in the suburban context, Patricia should pursue the steak restaurant option for suburban Los Angeles.

Part C: Calculation of Attribute Weights for Metropolitan Area

In a metropolitan LA area, location becomes three times as important as taste, and two times as important as price. Assign taste weight as 1, then location is 3, and price is 0.5 (since location is twice as important as price, and location is 3, then price = 3/2 = 1.5, but based on the ratios, more straightforwardly, if location is 3× taste, and location is 2× price, then taste = 1, location = 3, price = 1.5; total sum = 1 + 3 + 1.5 = 5.5). Normalized weights: taste = 1 / 5.5 ≈ 0.182, location = 3 / 5.5 ≈ 0.545, price = 1.5 / 5.5 ≈ 0.273.

Using the same attribute ratings as above, the utility calculations are:

Steak Restaurant Utility: (85×0.182) + (70×0.545) + (60×0.273) ≈ 15.47 + 38.15 + 16.38 ≈ 69.99

Pizza Restaurant Utility: (90×0.182) + (65×0.545) + (55×0.273) ≈ 16.38 + 35.42 + 15.02 ≈ 66.82

In this metropolitan context, the steak restaurant still has a higher utility; thus, Patricia should opt for the steak restaurant if opening in the metropolitan area.

Part D: Considering Probabilities and Decision Making

The likelihood of finding a venue varies with location: 0.7 for suburban and 0.3 for metropolitan. The expected value (EV) of each choice is calculated by multiplying the utility by the probability of success:

EV_suburban = Utility_suburban × 0.7

EV_metropolitan = Utility_metropolitan × 0.3

Using the earlier calculations:

EV_suburban = 72.23 × 0.7 ≈ 50.56

EV_metropolitan = 69.99 × 0.3 ≈ 21.00

Since the expected utility is higher for the suburban location, Patricia should prioritize establishing her restaurant there, considering the probabilities.

In real-world decision-making, this method reflects the importance of weighing different scenarios based on their likelihood and relative attractiveness. Scenarios like selecting a site for retail stores, choosing suppliers, or market segmentation strategies operate similarly, where attributes influencing success are modeled and weighted based on probability. This approach benefits decision-makers by adding a quantitative layer to choices, reducing bias, and clarifying trade-offs. However, it also has drawbacks, such as reliance on accurate probability estimates and attribute ratings, which can be subjective or uncertain, potentially leading to misguided decisions if inputs are inaccurate.

Problem 2: Demand Function and Price Elasticity of Newton’s Donuts

Part A: Calculating Quantity and Demand Parameters

The demand function is:

Qx = -14 – 54Px + 45Py + 0.62Ax

Given the current values: Ax=120, Px=0.95, Py=0.64.

Substituting these into the demand function:

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

Qx = -14 – 51.3 + 28.8 + 74.4 ≈ 37.9 thousand donuts

This indicates the current expected quantity demanded is approximately 37,900 donuts at the existing levels of advertising and prices.

Part B: Price Elasticity of Demand

The price elasticity of demand is computed as:

E_d = (dQ/dP) × (P / Q)

From the demand equation, the coefficient of Px is -54, so dQ/dP = -54.

Using current values, P = 0.95 and Q ≈ 37.9:

E_d = (-54) × (0.95 / 37.9) ≈ -54 × 0.025 ≈ -1.35

This elasticity of approximately -1.35 indicates that demand is elastic; a 1% increase in price would lead to about a 1.35% decrease in quantity demanded. This suggests that increasing the price could reduce total revenue, assuming other factors remain constant.

Part C: Inverse Demand Curve

Rearranging the original demand function to express Px as a function of Q:

Qx = -14 – 54Px + 45Py + 0.62Ax
=> 54Px = -14 + 45Py + 0.62Ax – Qx
=> Px = [–14 + 45Py + 0.62Ax – Qx] / 54

Substituting the known values:

Px = [–14 + 45(0.64) + 0.62(120) – Qx] / 54

Calculating numerator:

–14 + 28.8 + 74.4 = 89.2, so:

P_x = (89.2 – Q_x) / 54

Part D: Pricing Decision and Advertising Spending

Given the marginal cost of $0.15 per donut, the current price is $0.95, which yields a profit margin of $0.80 per donut. Since the demand is elastic, increasing the price would likely decrease total revenue and profit. Therefore, reducing the price could increase sales volume, potentially leading to higher overall profit, but only if the total revenue increases following the price decrease.

Regarding advertising, since the coefficient for advertising expenditure (0.62) is positive and significant, spending more on advertising would likely increase demand, shifting the demand curve outward, and could lead to higher sales volumes. Because the elasticity analysis shows demand is somewhat elastic, increased advertising might boost sales sufficiently to offset increased costs and generate higher profits. Therefore, it could be beneficial for Newton’s Donuts to increase advertising expenditure to stimulate demand and maximize revenues.

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