Name ID Fin 321 F2015 Homework 3 Credit

Name Id Fin 321 F2015 Hw 3 Credit W

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Cleaned Assignment Instructions

Apple considers itself a price leader in the mobile phone market, with other producers acting as followers. The total demand for mobile phones is given by P=22,500 - 5Q(T). Apple’s marginal cost function is MC(L) = 4,450 + 4.25Q(L), and the overall marginal cost function for the followers is MC(F) = 2,150 + 4.5Q(F).

Part A: Determine how many units Apple should produce to maximize profits and the price they should charge.

Part B: Find the total demand at the price set by Apple and the quantity supplied by followers.

Problem 2: Analyze a payoff matrix for a game of complementary investments between persons A and B. Determine if there are dominant strategies, identify any equilibria, and find the maxmin solution.

Problem 3: Ford and Honda are considering manufacturing electric cars. Given their payoff matrix, decide their optimal strategies and analyze how an incentive payment to Ford would impact their decision-making.

Problem 4: GoPro monopolizes the video camera markets in the USA and Canada with demand functions Q(USA)=105 - P(USA) and Q(Canada)=42.5 - 0.5P(Canada). The production cost per unit is $20, and cross-border resale is illegal. Find the equilibrium prices and quantities in both markets, and evaluate elasticity relationships.

Paper For Above instruction

This paper addresses multiple interconnected economic and strategic scenarios, including market behavior of Apple as a price leader, game theory analysis of investment decisions by two firms, competitive strategies in electric vehicle manufacturing, and pricing strategies under monopolistic control in international markets. Each problem involves applying fundamental concepts of microeconomics, game theory, and strategic pricing to derive optimal strategies, equilibrium outcomes, and market responses.

Part 1: Apple’s Market Leadership and Profit Maximization

Apple’s assertion as a price leader in the mobile phone market indicates that it sets prices knowing that competitors follow its lead. The demand function provided is P = 22,500 - 5Q(T), where Q(T) represents the total quantity demanded in the market. Apple’s marginal cost function is MC(L) = 4,450 + 4.25Q(L), while the followers’ marginal cost function is MC(F) = 2,150 + 4.5Q(F). Assuming that Apple and followers are producing quantities Q_A and Q_F respectively, the total market quantity Q = Q_A + Q_F.

To determine Apple’s profit-maximizing quantity, we consider the dominant position of Apple and its influence on the market. As the price leader, Apple sets its output where its marginal revenue (MR) equals its marginal cost. Given the linear demand, the total revenue (TR) for Apple is TR_A = P * Q_A, with P expressed as a function of total quantity. The price is a shared function in the market, so P = 22,500 - 5(Q_A + Q_F).

The marginal revenue (MR) for Apple can be derived from the total revenue function: TR_A = P Q_A = (22,500 - 5(Q_A + Q_F)) Q_A. Differentiating TR_A with respect to Q_A gives MR_A, which, after substitution for Q_F, allows setting MR_A = MC_L to find the optimal Q_A. Since the followers are acting as price takers with their own cost functions, their supply responds to the deviating price set by Apple.

By solving these equations simultaneously, Apple’s optimal quantity can be determined, and the corresponding market price obtained by substituting Q_A and Q_F into the demand function.

Specifically, Apple maximizes profit by selecting Q_A such that:

MR_A = MC(L) = 4,450 + 4.25Q_A

with MR_A derived from the demand elasticity:

MR_A = P + Q_A * (dP/dQ) = (22,500 - 5Q) - 5Q_A

Given the symmetry and the equilibrium conditions, the solutions involve setting these equations equal and solving for Q_A. The price charged is then calculated as P = 22,500 - 5(Q_A + Q_F).

Once Q_A is established, total market demand at the set price is obtained from the demand function, and followers supply their competitive quantities based on the marginal cost and the market price.

Part 2: Strategic Investment Choices – Payoff Matrix Analysis

The payoff matrix involves two individuals, A and B, who can choose to invest or not. The matrix, with payoffs, is typically as follows:

Analysis of the matrix involves identifying dominant strategies—choices that are optimal regardless of the other player’s action—and equilibria where both players’ strategies are mutually best responses. The maxmin strategy, which maximizes the minimum payoff, involves selecting the option that guarantees the highest payoff in the worst-case scenario.

In this case, suppose that investing yields a certain payoff (-A) and not investing yields a different payoff, with the structure suggesting potential dominance or neutral strategies. By analyzing the payoffs in each cell, we determine if any player has a dominant strategy (a choice that is better regardless of the other's decision), and hence identify any Nash Equilibrium.

If both players have a dominant strategy — for instance, both choose to invest or not invest— this configuration becomes a stable equilibrium. Otherwise, the equilibrium may be a mixed one, requiring further calculation.

The maxmin solution involves selecting the strategy that optimizes the minimum payoff obtainable, providing a conservative safety measure in strategic decision-making.

Part 3: Electric Vehicle Market Entry Decisions by Ford and Honda

The payoff matrix for Ford and Honda is analogous, with their strategic options being to enter or not. The payoffs reflect profits, market share, or strategic advantages under different choices:

When firms choose simultaneously, the best responses hinge on the payoffs associated with each combination. If both firms enter, the payoffs might indicate a competitive outcome, possibly less profitable than the scenario where only one enters or neither does.

Suppose the initial payoffs favor one firm entering, prompting strategic considerations about market competition versus cooperation, or potential collusion benefits.

Introducing a government subsidy of $55 million to Ford shifts its payoffs, incentivizing entry further. This external incentive effectively lowers Ford’s effective cost or increases its revenue, prompting a re-evaluation of its strategic decision. With the additional incentive, the prior equilibrium might change, resulting in both firms entering the market in the new scenario. The analysis involves comparing payoff differentials with and without the subsidy, and determining shifts in dominant strategies and equilibrium points.

Part 4: Monopolistic Pricing Strategies in International Markets

GoPro’s monopoly in the USA and Canada involves separate but related markets with demand functions:

• USA: Q(USA) = 105 - P(USA)
• Canada: Q(Canada) = 42.5 - 0.5 P(Canada)

Cost per unit is $20, and strict laws prevent resale across borders, making market segmentation essential. The optimal pricing strategy involves setting marginal revenue (MR) equal to marginal cost (MC). For each market, the inverse demand functions allow derivation of total revenue (TR), marginal revenue (MR), and then optimal prices and quantities.

In the USA, the revenue function is TR = P Q = P (105 - P). Differentiating TR with respect to Q or P yields MR. Setting MR = MC gives the profit-maximizing price and quantity: solving 4TR/dQ = 20. Similarly, for Canada, the demand function and revenue analysis yield the optimal price considering the elasticity of demand.

Elasticity relationships also confirm that the profit-maximizing prices are set where the elasticity of demand influences the markup over marginal cost, following the Lerner Index formula: Price = (Elasticity / (Elasticity + 1)) * MC. Both markets thus operate independently, with prices and quantities derived accordingly, satisfying economic efficiency and profit maximization goals.

In conclusion, the effective strategies involve setting higher prices in regions with less elastic demand, ensuring maximum profit margins while adhering to legal and logistical constraints.

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