Consider a duopoly market with a continuum of homogeneous consumers of mass 1. Consumers derive utility vi ∈ {v^H; v^L} for product i depending on whether the product is of high or low quality. Firms play the following 2- stage game: At stage 1, firms simultaneously invest in quality: The more a firm invests the higher is its probability λ_i of obtaining a high-quality product. The associated investment cost is denoted by I(λ_i) and satisfies standard properties that ensure an interior solution: I(λ_i) is continuous for λ_i ∈ [0, 1), I̅(λ_i) > 0 and I²(λ_i) > 0 for λ_i ∈ (0, 1), and lim λ ↓₀ I̅ (λ_i) = 0, lim λ ↑₁ I̅ (λ_i) = ∞. Before the beginning of stage 2 qualities become publicly observable- i.e., all uncertainty is resolved. At stage 2, …rms simultaneously set prices.

1. For any given (λ₁, λ₂), what are the expected equilibrium profits? In case of multiple equilibria select the (from the view point of the firms) Pareto-dominant equilibrium.

2. Are investments strategic complements or substitutes? Explain your finding.

3. Provide the equilibrium condition at the investment stage.

4. How do equilibrium investments change as v^H - v^L º Δ is increased?