ECOS2001 · Intermediate Microeconomics
General Equilibrium with Production
General equilibrium with production links the whole economy at once: outputs, inputs and prices must all be mutually consistent. The production possibility frontier shows the efficient output combinations; its slope is the marginal rate of transformation, the ratio of marginal costs, and overall efficiency requires MRT = MRS. Consumer incomes come from factor earnings plus profit shares. Walras' law says that if every market but one clears, the last clears automatically, so only relative prices matter and one price can be normalised. The signature high-mark final question follows a 5-step recipe: list markets, derive consumer demands and labour supply, derive firm input demands and profits, aggregate, then impose market-clearing to solve for the equilibrium relative prices. A social-planner Lagrangian reaches the same Pareto set as a dual.
What this chapter covers
- 01The PPF and the MRT as the ratio of marginal costs
- 02Efficiency condition MRT = MRS
- 03Consumer income = factor income + profit shares
- 04Walras' law: clear all-but-one market and the last clears; normalise a price
- 05The 5-step GE recipe for the high-value GE final question
- 06The social-planner dual delivering the same Pareto allocation
PPF and the marginal rate of transformation
- 2 marksDevote all labour to good 1: maximum x₁ = 100 / 2 = 50 units. This is the good-1 intercept.
- 2 marksDevote all labour to good 2: maximum x₂ = 100 / 5 = 20 units. This is the good-2 intercept.
- 1 markThe PPF is the straight line joining (50, 0) and (0, 20); its slope magnitude is 20/50 = 0.4.
- 1 markMRT = ratio of marginal (labour) costs = 2/5 = 0.4: one more unit of good 1 uses 2 labour, which would have made 2/5 of a unit of good 2.
Key terms
- Production possibility frontier (PPF)
- The boundary of efficient output combinations given fixed resources and technology; points inside are wasteful, points outside are infeasible.
- Marginal rate of transformation (MRT)
- The slope of the PPF, equal to the ratio of marginal costs; how much of one good must be given up to make one more unit of the other.
- Walras' law
- The total value of excess demand across all markets is zero, so if every market but one clears, the last must clear too — meaning only relative prices are determined.
- Social-planner dual
- An optimisation in which a planner maximises welfare subject to feasibility; its Lagrangian solution reproduces the same Pareto-efficient allocation as the competitive equilibrium.
General Equilibrium with Production FAQ
What is the efficiency condition that ties production to consumption?
MRT = MRS. The economy is fully efficient only when the rate at which it can transform one good into another (the PPF slope, MRT) equals the rate at which consumers are willing to trade them (their common MRS). If they differ, a reallocation makes someone better off.
Why can we normalise one price in a GE problem?
By Walras' law only relative prices are pinned down — scaling all prices up by the same factor leaves real choices unchanged. So we set one price (the numeraire) equal to 1 and solve for the others, which is also why one market-clearing condition is redundant.
Exam move
Memorise and rehearse the 5-step GE recipe end to end, because the high-value GE short-answer follows it; practise on one Leontief plus one Cobb-Douglas consumer with two simple firms. Always normalise a price and use MRT = MRS as your efficiency check.
