An economy comprises two consumers, 1 and 2, with two consumption goods bi-cycles (b) and wheat (w). Both consumers have the same utility function μ(b,w) = bw. Bi-cycles and wheat are produced by two firms which use only labor according to the production functions.
b=√1b and w= 0.5√1w
Both firms are owned by consumer 1, and consumer 2 owns 200 units of labour.
(a) Find the production possibility frontier for this economy.
(b) Find the competitive equilibrium.
(c) Find competitive equilibrium if every consumer owns 100 units of labour and owns one firm.
(d) Find the Pareto efficient allocations for this economy
(a) A production possibility frontier (PPF) is a graph representing production tradeoffs of an economy given fixed resources. The graph shows the various combinations of amounts of two commodities that an economy can produce (e.g., number of guns vs kilos of butter) using a fixed amount of each of the factors of production. Graphically bounding the production set for fixed input quantities, the PPF curve shows the maximum possible production level of one commodity for any given production level of the other, given the existing state of technology. (b) In this case, the competitive equilibrium can't be found, as there is not enough data. (c) If every consumer owns 100 units of labour and owns one firm, the competitive equilibrium will change. (d) We can't find the Pareto efficient allocations for this economy, because there is not enough data.