An economy comprises two consumers, 1 and 2, with two consumption goods bi-cycles (b) and
wheat. Both consumers have the same utility function μ (b,w) = bw
Bi-cycles and wheat
are produced by two firms which use only labour according to the production functions
b = root 1b and w = 0.5 root 1 w
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
(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. 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.