The Total Cost Function Is As Follows: Tc = 20 + 4q Calcula

The Total Cost Function Is As Follows Tc 20 4qcalcula

The assignment involves analyzing various economic scenarios and calculations, including cost functions, demand elasticity, price discrimination, project profitability under uncertainty, pricing strategies with moral hazard issues, auction bidding strategies, used car market dynamics, game theory in advertising, differential pricing based on demand elasticity, and strategic technology adoption between firms. Specifically, tasks include calculating fixed and variable costs, elasticities, profit-maximization prices, expected profits under uncertainty, optimal bidding strategies, market outcomes based on quality information, game-theoretic equilibria, and strategic incentives for technology adoption.

Paper For Above instruction

The comprehensive analysis of these economic and strategic scenarios offers valuable insights into firm decision-making processes, market dynamics, and consumer behavior. Below is a detailed exploration of each problem, integrating theoretical principles with practical applications.

Cost Analysis and Demand Elasticity

Starting with the total cost function TC = 20 + 4Q, calculating costs at Q=10 yields: total fixed cost (TFC), total variable cost (TVC), average total cost (ATC), and average fixed cost (AFC). The fixed cost is the constant component of total costs, which is $20 regardless of output. The variable cost at Q=10 is 4 x 10 = $40, thus the total cost at Q=10 is $20 + $40 = $60. The average total cost (ATC = TC/Q) becomes $60 / 10 = $6. Fixed cost per unit (AFC = TFC/Q) amounts to $20 / 10 = $2, and the average variable cost (AVC = TVC/Q) is $40 / 10 = $4. These calculations assist managers in understanding cost structures vital for pricing and output decisions.

Price Elasticity of Demand and Profitability

In the case of George selling T-shirts, the initial revenue at 5,000 units priced at $8.50 is $42,500. After increasing the price to $9.50, sales fall to 4,000 units, generating revenue of $38,000. The price elasticity of demand (PED) is calculated as:

PED = (% change in quantity demanded) / (% change in price) = [(4000 - 5000) / 5000] / [(9.50 - 8.50) / 8.50] = (-0.2) / (0.1176) ≈ -1.70.

This inelastic demand suggests that the price increase reduces total revenue, indicating that raising the price was not profitable in this context. Firms must consider elasticity when setting prices to optimize revenue.

Price Discrimination and Profit Maximization

Considering the gas station scenario, demand elasticity for BC residents is -2, and for non-BC residents, -1.5, with a marginal cost of $6. Price discrimination is feasible if the firm can segment markets and prevent arbitrage. Calculating profit-maximizing prices involves the inverse elasticity pricing rule:

P = (|elasticity| / (|elasticity| - 1)) * MC.

For BC residents: P_BC = (2 / (2 - 1)) 6 = 2 6 = $12. For non-BC residents: P_NBC = (1.5 / (1.5 - 1)) 6 = (1.5 / 0.5) 6 = 3 * 6 = $18. These prices reflect maximizing profits given elasticities and the ability to segment markets effectively.

Strategic Project Choice Under Market Entry Risk

A manager faces two projects with different profit profiles based on market entry by rivals. The expected profits are computed as:

For the new product: 0.2 x $80,000 + 0.8 x $60,000 = $16,000 + $48,000 = $64,000.

For revamping: 0.2 x $50,000 + 0.8 x $60,000 = $10,000 + $48,000 = $58,000.

The manager should pursue the new product, given its higher expected profit ($64,000 versus $58,000), aligning strategic choice with maximizing expected value under uncertainty.

Pricing Extended Warranties and Moral Hazard

The company's product fails approximately 2% of the time. Pricing the warranty at 2% of the product's price can be analyzed through the lens of moral hazard and adverse selection. If customers perceive the warranty as cheap, it may encourage overuse (moral hazard), increasing claim costs. Additionally, adverse selection occurs if only high-risk customers purchase the warranty, raising costs further. Setting the premium at 2% might be optimal if this balance minimizes expected costs and discourages excessive claims, but must be complemented with usage restrictions and risk assessments to mitigate moral hazard and adverse selection.

Optimal Bidding Strategies in Private Auctions

For bidders with valuations uniformly distributed between $100 and $1,000, the optimal bidding strategies are derived as follows:

• First-price, sealed-bid auction: The optimal bid is b = v – (v –最低价)/ (n + 1), which simplifies to approximately 66.7% of the valuation, resulting in about $600 for valuation of $900.
• Dutch auction: The bidder should bid just below the expected clearing price, typically bidding slightly above the valuation's lower bound, but strategic bid shading still applies.
• Second-price, sealed-bid auction: The dominant strategy is to bid one's true valuation ($900) because the winner pays the second-highest bid.
• English auction: The optimal bidding is to stay in until the bid surpasses the bidder's valuation, but as the last bidder, bidding one's true valuation is optimal.

Market for Used Cars with Asymmetric Information

In a market where high-quality Toyota Corollas are worth $10,000 and low-quality ones $5,000, with 25% of cars being high quality, the market features adverse selection. The expected value of a randomly selected car is:

E[V] = 0.25 x $10,000 + 0.75 x $5,000 = $2,500 + $3,750 = $6,250.

Car sellers of high-quality vehicles are willing to sell above $6,250, but low-quality ones will not, leading to a market primarily selling low-quality cars at prices close to $5,000, unless mechanisms like warranties or certifications are employed to mitigate information asymmetry.

Advertising Strategies and Nash Equilibrium

Considering the payoffs, the normal form of the game is tabulated below:

Dominant strategies are identified by comparing payoffs; both firms tend to advertise, resulting in a Nash equilibrium at both advertising, as each firm's best response to the other's strategy is to advertise.

Pricing Different Customer Segments

Knowing that the demand elasticity for young farmers is -2 and for retired families -4, the pricing strategy should reflect price sensitivity. Setting higher prices for less price-sensitive customers (young farmers) maximizes profits, while lower prices for more elastic retired customers encourage purchases. Dynamic pricing or segmentation can optimize revenue streams.

Strategic Technology Adoption Between Firms

In the technology adoption game, the payoffs depend on the fixed setup cost C. If AMD observes Intel adopting the new tech, AMD's incentive to adopt depends on whether the subsequent payoff exceeds the payoff if it refrains. If C is small enough, AMD will prefer to copy the technology to avoid losing competitive advantage. For C = 12, since AMD’s payoff when copying with C/2 ≤ $15, which is higher than the payoff of $2 if it does not adopt, AMD has an incentive to adopt if the fixed cost is below a certain threshold, reinforcing strategic investment decisions.

Conclusion

These scenarios demonstrate the importance of economic reasoning, strategic thinking, and data-informed decision-making in various market environments. From cost management to strategic bidding and technology investment, applying fundamental economic principles enables firms to optimize outcomes amid uncertainties and competitive pressures.

References

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