(a) (3%) For what condition (in terms of α, β, γ) would this production function exhibit constant returns to scale?

題組內容

5. A price-taking firm in a perfectly competitive market uses three factors of production: labor (L), capital (K), and material (K). The firm's faces the production function $Q(L, K, M) = L^{\alpha} K^{\beta} M^{\gamma}$ with $\alpha, \beta, \gamma > 0$. (15%)

(b) Show that if no one provides human right protection, one citizen among those who highly value human right has incentive to unilaterally deviate from providing zero human right protection.Please characterize the above Nash equilibrium. Specifically, how many citizens provide human right protection? Who is(are) the provider(s)? In equilibrium, what is the actual level of human right protection in the society?$^2$ For example, if Citizen 1 provides r1 = 0.1 and Citizen 2 provides r2 = 0.7, and no one else provides positive level of human right protection, the actual level of human right protection in the society is $r = \max\{r1, r2\} = 0.7$.

題組內容

(a) \( (3\%) \) For what condition (in terms of \( \alpha, \beta, \gamma \)) would this production function exhibit constant returns to scale?

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