In Depth Notes on Monopolist's Advertising and R&D Competition

Monopolist Demand Function:

Q_d = D(P) , where:

• Demand decreases as price (P) increases for a given advertising level (A). This indicates that consumers are sensitive to price changes; as prices rise, they purchase less.

• Conversely, demand increases as advertising (A) increases for a given price (P). This suggests that effective advertising can enhance consumer interest and encourage higher purchase volumes.

Cost Function:

C(A) = C_0 + cA , where:

• C(A) is the total cost which encompasses both fixed costs (C_0) and variable costs associated with advertising expenditures.

• The term 'c' reflects the cost per unit of advertising, which includes costs such as media buys, production, and other related expenses. Businesses must manage these costs efficiently to maximize profitability.

Profit Maximization Objective:

The monopolist seeks to maximize profits through the determination of optimal advertising level (A) and price (P).

• Profit can be expressed as
  
  ext{Profit}(P, A) = Revenue(P, A) - Cost(A)
  

• Revenue is influenced by both price and demand generated through advertising efforts, requiring a careful balance for optimization.

Profit Maximization Conditions

First Order Conditions (FOC) for maximum profit:

1. Price Relation at the margin:

MR = MC

• Here, MR represents Marginal Revenue, indicating the additional revenue derived from selling one more unit; MC denotes Marginal Cost, costing one extra unit of production. This condition ensures the firm does not expand output profitably beyond this point.

1. Advertising Relation at the margin:

MRA = MCA

• MRA is the marginal return on advertising, measuring the increase in demand resulting from a marginal increase in advertising; MCA is the marginal cost of advertising, which evaluates the cost associated with a marginal increase in advertising.

Rearranging FOC provides a critical relationship:

rac{dQ}{dA} = C'(A)

• This equation connects the change in quantity demanded to the expenditures on advertising, demonstrating that effective advertising must be assessed against its costs.

Dorfman-Steiner Condition

When rearranged, it gives:

rac{ ext{Advertising expenditure}}{ ext{Sales Revenue}} = ext{elasticity}

• This condition implies that higher monopoly power correlates with increased advertising expenditure. It emphasizes the significance of advertising as a tool to leverage market position while being aware of the elasticity of demand.

Motivation and R&D Questions

Firms must continuously evaluate key questions regarding the R&D process, including:

• How can the firm enhance its market position through innovation and strategic R&D initiatives?

• Which market structures (monopoly, oligopoly, perfect competition) provide the best environment for encouraging R&D? Understanding this can guide investment strategies.

Simple Model of Innovation Race

Two Firm Model:

• Each firm can invest an amount (£F) into R&D. The strategic decisions firms make regarding these investments can impact market dynamics significantly.

• If the discovery is certain, profits from discovery are computed as:
  ext{Profits} = P( ext{Profits}M, ext{Profits}C)

Understanding Uncertainty:
Profit outcomes are influenced by several key probabilities:

• The probability of discovering technology (p) plays a critical role.

• Potential outcomes include:

  • Sole discoverer: Profit = £ΠM

  • Both firms discover: Profit = £ΠC

  • No discovery: Profit = £0

• This uncertainty drives firms to make calculated risk assessments regarding their R&D investments.

Expected Profit Model:
For both firms, the expected profit can be framed as:
EPD_{duopole} = p(1 - p)ΠM + p^2ΠC - F

• Firms will only invest in R&D if expected profits (EPD) are positive (i.e., EPD > 0). This ensures that resources are allocated to viable innovational pursuits.

R&D/Product Competition Models

Key Models:

1. KMZ Model: Focuses on strategies for cost reduction driven by R&D investment efficiency.

2. AJ Model: Highlights how costs of production are influenced by R&D investments, illustrating the interplay between R&D and product pricing.

Schumpeter's Theory:

• Larger firms are often viewed as driving innovation due to their heightened market power, given their ability to invest substantially in R&D.

Arrow's Insight:

• Perfect competition may enhance innovation incentives compared to monopoly structures, advocating for environments where numerous competitors drive creativity and technological advancement.

Correlation between Concentration and Innovation:

• Market structure significantly impacts levels of R&D investment; however, establishing a causal relationship can be complex due to various external economic factors and incentives.