Micro

• General Equilibrium


  Describes how consumers and producers, each acting independently in pursuit of self-interests, interact in a way such that their decisions are in line with prevailing prices
• Walrasian equilibrium


  The final outcome - a set of prices and associated quantities whereby all economic agents are induced to make privately optimal decisions that are all consistent with one another
• Necessary conditions for General Equilibrium

  • Each household/consumer chooses consumption that is utility-maximising, subject to budget constraint
  • Each firm/producer chooses production that is profit-maximising, subject to production function
  • Profit distributed to households according to some rule
  • Market clearing: for each good, total supply equals total demand
• Walras Law


  The value of excess demands totals up to zero, implying that if equilibrium is achieved in N-1 markets, the last market is in equilibrium too
• Assumptions in the basic general equilibrium model: 1 country, 1 time period, no uncertainty, no government, all economic agents are price-takers, no market power, exogenous q/H/F/N
• Applications of General Equilibrium

  • Informs economists of the full equilibrium effects caused by an exogenous change
  • Serves as a foundation that underpins important macroeconomic models
• Example of basic general equilibrium: 2 goods (output x, leisure l), 1 producer, 1 consumer


  • Firm: chooses xs and ld to maximise profit, subject to production function
  • Consumer: chooses xd and ls to maximise utility, subject to budget constraint
  • Equilibrium: point where production function intersects highest isoprofit line and budget constraint intersects highest utility curve
• Varying relative prices traces out supply and demand curves in the general equilibrium example
• Will return to technicalities: now assume a solution exists
• GCE: eg #1: 2 goods, 1 producer, 1 consumer

  • Goods: output x, labour l
  • Producer choice: Choose xS, lD to maximise π = pxS - wlD subject to xS = F(lD)
  • Value marginal product of labour = wage: pF'(lD) = w
  • Input demand function: lD =LD(w/p)
  • Output supply function: xS = XS(w/p) = F(LD(w/p))
  • Maximised profits: π = П(w,p) = p[F(LD(w/p)) – (w/p)LD(w/p)]
• Varying relative price


  Traces out supply and demand curves
• Iso-profit line


  • π = pxS - wlD
  • Production fn. xS = F(lD)
• GCE : eg #1: 2 goods, 1 producer, 1 consumer


  • Consumer choice: Choose xD, lS to maximise u(xD , l0 - lS) subject to pxD = wlS +M
  • Marginal rate of substitution = price ratio: MRS ≡ (∂u / ∂l) / (∂u / ∂x) = w/ p
  • Labour supply function: lS = LS(w/p,M)
  • Product demand function: xD = XD(w/p,M)
• Varying relative prices


  Trace out supply and demand curves
• Equilibrium occurs when


  • Firm's profit is transferred to household as wealth: π(w,p) = M
  • All markets clear: xs = xd ; ls = ld
  • Price mechanism has allowed for the coordination of private plans of both households and firms
• In the event of disequilibrium, excess supply / demand will exert pressure on w/p to restore equilibrium
• Case 2 – 'exchange economy': 2 goods (1 & 2), 2 agents (A & B)


  • Each agent owns an initial endowment of each good
  • Each consumer wishes to maximise own utility, u(cA1, cA2) and u(cB1, cB2), subject to their budget constraints p1cA1 + p2cA2 = p1eA1 + p2eA2 and p1cB1 + p2cB2 = p1eB1 + p2eB2
  • Equilibrium occurs when the total sum of goods agents wish to consume equals the total sum of goods agents were endowed with (cA1 + cB1 = eA1 + eB1; cA2 + cB2 = eA2 + eB2), allowing the markets for both goods to clear
• Case 3 – 'specific factors': 2 producing sectors, 1 consumer


  • Input factor of labour is fixed at L; two industries producing two goods 1 & 2 with production functions y1 = G1(L1) and y2 = G2(L2)
  • Factor market clearing: L = L1 + L2
  • Each firm chooses Li to maximise π = pGi(Li) - wLi
  • Each consumer chooses c1, c2 to maximise u(c1, c2), subject to budget constraint p1c1 + p2c2 = wL + π1 + π2
• In closed economy, equilibrium achieved at: MRS = MRT = p1/p2, c1 = y1, c2 = y2, w = pGi'(Li)
• Disequilibrium


  • Figure has w/p less than the equilibrium value
  • Positive excess demand for labour
  • Negative excess demand for good x
  • 'Auctioneer' raises w/p
• • Walras' law: Value of excess demands sums to zero, w.(lS - lD)= p.(xD - xS)
  • Implies that: If equilibrium in N-1 markets, must be equilibrium in Nth
  • Only N -1 independent equations
  • Set one price as the numeraire (only relative prices matter)
• GCE: eg #2: 2 goods, 2 consumers, exchange economy (no production)


  • Goods: 1, 2
  • Consumers, a, b
  • Endowments: {ea1, ea2}, {eb1, eb2}
  • Consumers' budgets: p1(ca1 - ea1) + p2(ca2 – ea2) = 0, p1(cb1 - eb1) + p2(cb2 – eb2) = 0
  • Consumers' choice: Chose ca1, ca2 to max ua (ca1, ca2 ) s.t. budget, Chose cb1, cb2 to max ub (cb1, cb2 ) s.t. budget
  • Equilibrium: p1/p2 such that ca1 + cb1 = ea1 + eb1 (and by Walras' law, ca2 + cb2 = ea2 + eb2)
  • Contract curve: Locus of points where MRSa = MRSb
• GCE, eg #3: The specific-factors model: 2 producing sectors, 1 consumer


  • Endowment of labour: L, (fixed)
  • Output goods: 1, 2
  • Technology: yi = Gi(Li), for i = 1, 2
  • Factor market clearing: L1 +L2 = L
  • Producers: Maximise πi = pi Gi(Li) – wLi
  • Consumer: Indifference curve: u(c1, c2)
  • Budget line: p1 c1 + p2 c2 = p1 y1 + p2 y2 = w(L1 +L2)+ π1+ π2
  • Closed economy: S = D, c1 = y1 , c2 = y2
  • Equilibrium prices: MRS12 = p1/ p2 = MRT12, w = pi G'i(Li)
• When economy is open for trade, agents are exposed to a new set of 'world prices': p1W, p2W
• Depending on the exact ratio p1W/ p2W, an economy may have comparative advantage (CA) in either good 1 or 2


  It will then proceed to export the good in which it has a comparative advantage
• CA stems from differences in relative prices and not absolute ones; countries with absolute disadvantages across all sectors will still stand to benefit from trade
• While trade leads to aggregate gains, there will probably be specific losers as well
• Determinants of CA include labour productivity, the presence of fixed inputs, factor endowments
• Comparative Statics


  • Effects of a simple change can be demonstrated by altering FOCs accordingly and solving for a new general equilibrium
  • Example: Exogenous increase in the price of one good leads to a shift in labour allocation, change in profits and ambiguous impact on real wage
• Repeal of Corn Laws in 1846 eliminated high import tariffs on corn and dealt a heavy blow to domestic corn prices, reducing profit of landowners and increasing that of factory owners
• A general equilibrium may not always exist; having N-1 equations in N-1 unknowns does not necessarily guarantee a solution
• In order for there to be a general equilibrium, supply and demand functions ought to be continuous in prices
• Optimisation problems must be concave – need to check for second-order conditions
• The non-existence of general equilibria could also mean that the underlying assumptions behind the GCE theory did not hold – for example, 'distortions' such as externalities, imperfect competition and informational asymmetries could all lead to complications
• Multiple equilibria


  • Could be many solutions – multiple equilibria
  • Policy change might shift economy from one equilibrium to another – not just comparative statics
• Continuity


  • Requires that optimisation problems are concave (satisfy 2nd order conditions)
• Set of assumptions not consistent with equilibrium
• Insight into circumstances in which price system can decentralise decisions
• See an example in economics of imperfect information
• Further reading: Nicholson and Snyder (p. 455-463)