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An economy is composed of two industries x and y, one labour market L and two consumers A and B. The industry includes a firm whose production function is gy(Ly) = Ly. Industry x includes a firm whose production function is fx(Lx) = (Lx)^1/2 . Consumer A has utility function UA(xA; yA) and B, UB(xB; yB).
The economy is endowed with a quantity L of work. It is assumed that good x is a public good.
(i) Give all the conditions to characterize the effective allocations of this economy.
(ii) Assume that each consumer has half the work allowance L as well half of each company's shares. Also assume that the labour market andthe two industries x and y are competitive. Give all the conditions to characterize a general balance of this economy.
(iii) Discuss the efficiency properties of the general equilibrium of this economy.
(iv) Now suppose that firm x is a monopoly. If the government wanted to intervene to restore efficiency in this economy, explain what should be considered so that an optimal policy can be implemented.
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