Problem Set 1: Nestlé’s Has Over One Hundred Production Faci ✓ Solved

Problem Set1 Nestlé’s Has Over One Hundred Production Facilities That

Problem Set 1. Nestlé’s has over one hundred production facilities that all purchase hair nets and other hygienic supplies through independent suppliers. Nestlé created a centralized purchasing system that is cumbersome to use has the potential to bargain for lower prices. Suppose that a division can purchase hairnets for $8 independently. If they all purchase through the central system, hairnets cost $6. But if one division uses the system and the other purchases independently, the cost to the first is $9 while the cost to the second is $7. What does the simultaneous move game look like and what is the equilibrium?

2. The Doug’s Delicious Diner faces a demand curve for its daily special in which there are an equal number of potential buyers at every $0.20 price point between $8.00 and $6.00. If the marginal cost is $6.35, what price maximizes profits? Doug notices that at this price the unserved portion of demand are all senior citizens. If it offered a senior discount, how much should it be?

Sample Paper For Above instruction

Introduction

In this paper, we analyze two distinct economic scenarios involving strategic decision-making and optimal pricing strategies. The first scenario explores a classic game theory model concerning procurement strategies within Nestlé's large-scale operations. The second examines optimal pricing decisions for a restaurant balancing demand, marginal cost, and targeted discounts for specific customer segments.

Part 1: Game Theoretic Analysis of Nestlé's Procurement Strategies

Nestlé operates over one hundred production facilities, each faced with the decision to purchase hygienic supplies either independently or through a centralized system. The central question involves understanding the strategic interactions between divisions when choosing procurement methods.

The payoff matrix delineates the costs associated with various strategies:

• If all divisions purchase independently, the per-unit cost is $8.
• If all divisions use the central system, the cost drops to $6.
• If one uses the central system while others purchase independently, the scenario becomes asymmetric: the buyer using the system faces a cost of $9, whereas the independent buyer faces $7.

This setup mirrors a simultaneous move game where each division's choice impacts the others' costs, and equilibrium analysis hinges on identifying stable strategies where no division benefits from unilateral deviation.

Game Representation

The strategic choices for each division are "Use Central System" (C) or "Purchase Independently" (I). The payoff matrix can be summarized as follows:

Analyzing this matrix reveals the best response strategies and potential equilibria.

Equilibrium Analysis

In the matrix, the strategy profiles where neither division can improve their outcome by switching unilaterally are considered Nash equilibria. Notable observations include:

• Both divisions purchasing independently (I, I) results in costs of $8 for each, which could be unstable if divisions anticipate the potential for lower costs via cooperation.
• The profile (C, C) yields costs of $6 for both, representing a favorable stable state if cooperation is enforced or incentive-compatible.
• Mixed strategies involve divisions randomizing between options, but without binding agreements, the equilibrium likely gravitates toward (C, C) or (I, I), based on payoffs and negotiations.

Part 2: Optimal Pricing for Doug’s Delicious Diner

Doug’s Delicious Diner is facing a demand curve with uniform customer distribution across prices ranging from $8.00 to $6.00 at $0.20 intervals, indicating demand at each price point is equal.

Demand Structure

The prices are: $8.00, $7.80, $7.60, $7.40, $7.20, $7.00, $6.80, $6.60, $6.40, $6.20, and $6.00.

Given this, the total number of potential buyers is consistent across these prices, but actual demand depends on the chosen price.

Profit Maximization

The marginal cost of the special is $6.35. To maximize profit, Doug’s needs to select a price that maximizes total profit, calculated as (Price – Marginal Cost) × Quantity demanded at that price.

Since demand at each price point is equal, the optimal price is one that balances higher margin with sufficient volume.

Determining the Best Price

Calculations suggest that the profit is maximized at the highest price where demand remains positive and marginal costs are covered, likely near or above $7.20.

Targeting Senior Citizens with a Discount

If the unserved demand at the profit-maximizing price consists mainly of senior citizens, Doug’s should offer a discount to encourage their patronage. The discount should be carefully calibrated to attract this segment without eroding profit margins excessively.

Typically, a discount roughly equal to the difference between the current price and the marginal cost, say around $0.50 to $1.00, could be appropriate. This could mean setting a discount price near $6.20 or $6.50.

Conclusion

Strategic procurement decisions in large corporations like Nestlé can be effectively modeled by game theory, highlighting the importance of cooperation and strategic interactions. Meanwhile, dynamic pricing strategies in restaurants should consider demand structure, costs, and target segments to optimize profits. Both cases demonstrate the critical role of economic analysis in decision-making processes.

References

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Note:

This comprehensive analysis provides insights into strategic procurement, pricing optimization, and targeted marketing strategies, essential in today's competitive business environment.