Difficulty: Intermediate-Advanced | Prerequisites: Consumer theory, producer theory, supply and demand.
General equilibrium and welfare economics ask whether markets, taken as a whole, allocate resources well. The Edgeworth box shows how two agents can trade to a mutually beneficial outcome, and the First Welfare Theorem tells us that competitive equilibria are Pareto efficient. Tax incidence and deadweight loss analysis show what happens when the government intervenes in an otherwise competitive market. You need consumer theory (utility maximisation, demand functions) and basic supply-and-demand analysis as prerequisites.
In a pure exchange economy, the competitive equilibrium price ratio is found by deriving each agent's demand from their endowment income and clearing markets. The First Welfare Theorem guarantees that this equilibrium is Pareto efficient. When a government imposes a tax, quantity traded falls, a wedge opens between buyer and seller prices, and the lost surplus that neither party nor the government captures is deadweight loss.
Edgeworth box
A diagram representing all possible allocations of two goods between two agents. Each point in the box is a feasible allocation. The box's dimensions are set by total endowments of each good.
Think of it as a map of every way two people could split two piles of stuff.
Pareto efficiency (Pareto optimality)
An allocation where no one can be made better off without making someone else worse off. On the Edgeworth box, Pareto-efficient allocations lie along the contract curve.
In simple terms, there is no free lunch left on the table.
Contract curve
The set of all Pareto-efficient allocations in the Edgeworth box, where the agents' indifference curves are tangent to each other (MRS_A = MRS_B).
Think of it as the line of "best possible deals" between the two agents.
Competitive equilibrium (Walrasian equilibrium)
A price ratio and allocation where each agent maximises utility given their budget (valued at equilibrium prices) and all markets clear.
In simple terms, it is the price at which supply equals demand for every good simultaneously.
First Welfare Theorem
Under certain conditions (no externalities, complete information, competitive markets), any competitive equilibrium is Pareto efficient.
In simple terms, if markets work properly, the outcome is efficient.
Endogenous variable
A variable determined within the model (e.g. equilibrium price and quantity). Contrast with exogenous variables, which are inputs to the model (e.g. tastes, endowments, technology).
Think of it as the thing the model solves for.
Tax incidence
How the burden of a tax is divided between buyers and sellers. It depends on the relative elasticities of demand and supply, not on who the tax is legally imposed upon.
In simple terms, the side of the market that is less responsive to price changes bears more of the tax.
Deadweight loss (DWL)
The reduction in total surplus caused by a market distortion (such as a tax). It represents the value of trades that would have happened in the absence of the distortion but no longer occur.
Think of it as the economic value that simply vanishes, collected by nobody.
Marginal Rate of Transformation (MRT)
The rate at which the market allows a consumer to exchange one good for another. In a consumer's problem, it equals the slope of the budget constraint, -Px/Py.
In simple terms, it is the market's exchange rate between two goods.
Two agents (A and B), two goods (x and y).
Each agent has an endowment (e.g. A has all of good x, B has all of good y).
Each agent's income equals the value of their endowment at market prices: M_A = Px * endowment_A_x + Py * endowment_A_y.
Derive each agent's demand functions from their utility function and endowment income.
Apply market clearing: total demand for each good equals total endowment.
Solve for the equilibrium price ratio Px/Py.
By Walras' Law, if one market clears, the other clears automatically.
U_A = x_A * y_A, endowment_A = (10, 0). U_B = x_B * y_B, endowment_B = (0, 10).
M_A = 10Px. With Cobb-Douglas (equal exponents), A spends half on each good: x_A = M_A/(2Px) = 5, y_A = M_A/(2Py) = 5Px/Py.
M_B = 10Py. Similarly: x_B = 5Py/Px, y_B = 5.
Market clearing for x: x_A + x_B = 10. So 5 + 5(Py/Px) = 10, giving Py/Px = 1, i.e. Px/Py = 1.
At this price ratio, Agent A consumes (5, 5) and Agent B consumes (5, 5).
States that any competitive equilibrium allocation is Pareto efficient.
Conditions required: no externalities, complete information, competitive (price-taking) behaviour.
This is a theorem about efficiency, not equity. The equilibrium may be very unequal but still Pareto efficient.
General equilibrium analysis underlies computable general equilibrium (CGE) models used by governments and international organisations to forecast the economy-wide effects of trade agreements, tax reforms, and climate policies.
A specific tax of t dollars per unit on sellers shifts the supply curve up by t (or equivalently, the price sellers receive is Pd - t, where Pd is the price buyers pay).
The new equilibrium has a higher buyer price, a lower seller price, and a lower quantity traded.
The economic burden of the tax is split between buyers and sellers according to the relative elasticities of demand and supply.
The more inelastic side bears more of the tax. If demand is perfectly inelastic, buyers bear the entire tax.
Tax incidence does not depend on whether the tax is legally imposed on buyers or sellers.
DWL is the triangle of lost surplus between the old and new equilibrium quantities.
Formula: DWL = 0.5 * (Q_initial - Q_tax) * t.
DWL arises because mutually beneficial trades (those between Q_tax and Q_initial) no longer happen.
Demand: Qd = 40 - 2P. Supply: Qs = 2P - 8. Tax: t = $4 on sellers.
Initial equilibrium: 40 - 2P = 2P - 8, so 4P = 48, P = 12, Q = 16.
With tax, invert supply to get Ps = 4 + 0.5Q. Sellers now need Pd = Ps + t, so the effective supply becomes Pd = 8 + 0.5Q.
New equilibrium: 20 - 0.5Q = 8 + 0.5Q, so Q_tax = 12.
DWL = 0.5 * (16 - 12) * 4 = 0.5 * 4 * 4 = 8.
Deadweight loss analysis is central to public finance. It is why economists generally favour broad-based taxes with low rates (which create small DWL triangles) over narrow taxes with high rates (which create large ones). The same framework applies to tariffs on imports.
\text{Endowment income: } M_i = P_x \cdot \omega_{i,x} + P_y \cdot \omega_{i,y}\text{Market clearing: } x_A + x_B = \bar{x}, \quad y_A + y_B = \bar{y}\text{Pareto efficiency in Edgeworth box: } MRS_A = MRS_B\text{Deadweight loss: } DWL = \frac{1}{2} \times (Q_{\text{initial}} - Q_{\text{tax}}) \times t\text{MRT (consumer setting): } -\frac{P_x}{P_y}Students often think Pareto efficiency means fairness or equality. An allocation where one person has everything and the other has nothing can be Pareto efficient, as long as you cannot improve one person's situation without worsening the other's.
Students often think tax incidence depends on who the tax is levied on (buyers vs. sellers). The economic burden is determined by relative elasticities, not by the legal assignment of the tax.
Students often compute DWL using the wrong formula. DWL is 0.5 * change in quantity * tax, not 0.5 * tax * original quantity. The triangle's base is the reduction in quantity, not the original quantity.
Students often think the MRT is the slope of the indifference curve. The MRT is the slope of the budget constraint (or the production possibilities frontier in a production economy). The MRS is the slope of the indifference curve.
⚠️ The Edgeworth box / competitive equilibrium problem (derive demands, clear markets, find price ratio and allocation) is a standard 10-mark question.
⚠️ Stating the First Welfare Theorem precisely (competitive equilibrium is Pareto efficient, given no externalities and complete information) is a common 2-mark question.
⚠️ Tax incidence and DWL calculation (find initial equilibrium, shift supply by tax, find new equilibrium, compute the DWL triangle) is heavily tested.
⚠️ Know that MRT = slope of budget constraint = -Px/Py. This is a multiple-choice staple.
⚠️ Pareto efficiency = "no one better off without someone worse off." Do not confuse it with equality.
True or False: A Pareto efficient allocation must be equitable. (False.)
Fill in the blank: By Walras' Law, if one market clears in a two-good economy, the other market ______. (Also clears.)
True or False: In a competitive market, a tax on producers always results in producers bearing the full burden. (False. Burden depends on relative elasticities.)
Fill in the blank: The MRT in a consumer's problem equals ______. (-Px/Py, the slope of the budget constraint.)
True or False: Deadweight loss from a tax is collected by the government. (False. DWL is surplus lost to nobody.)
Q: In a pure exchange economy, agents A and B both have utility U = x*y. A's endowment is (10, 0) and B's is (0, 10). Find the equilibrium price ratio and A's allocation.
A: M_A = 10Px. Demands: x_A = 5, y_A = 5Px/Py. M_B = 10Py. Demands: x_B = 5Py/Px, y_B = 5. Market clearing for x: 5 + 5Py/Px = 10, so Py/Px = 1, i.e. Px/Py = 1. A consumes (5, 5).
Q: Demand is Qd = 40 - 2P, supply is Qs = 2P - 8, and a $4 per-unit tax is imposed on sellers. Find the initial equilibrium quantity and the DWL.
A: Initial: 40 - 2P = 2P - 8, P = 12, Q = 16. With tax: new supply price = 8 + 0.5Q. Setting equal to demand price 20 - 0.5Q: Q_tax = 12. DWL = 0.5 * (16 - 12) * 4 = 8.
Q: State the First Welfare Theorem.
A: Under certain conditions (no externalities, complete information), any competitive equilibrium (where markets clear) is Pareto efficient.
Q: The MRT corresponds to: (a) slope of the indifference curve, (b) slope of the budget constraint, (c) ratio of marginal utilities, (d) curvature of the isoquant.
A: (b) The slope of the budget constraint.
Q: In a competitive market, a tax on producers usually results in: (a) lower consumer prices, (b) higher quantity, (c) deadweight loss, (d) higher producer surplus.
A: (c) The creation of a deadweight loss.
General equilibrium ties together consumer theory (each agent's demand comes from utility maximisation) and producer theory (in a production economy, firms' profit maximisation feeds into supply). The First Welfare Theorem connects to market-structure analysis: it holds under perfect competition but breaks down with monopoly, externalities, or asymmetric information. Tax incidence and DWL analysis directly extend the supply-and-demand framework from introductory micro, and the DWL concept reappears in monopoly welfare analysis.
General equilibrium, Edgeworth box, pure exchange economy, competitive equilibrium, Walrasian equilibrium, Pareto efficiency, Pareto optimality, contract curve, First Welfare Theorem, Second Welfare Theorem, Walras' Law, market clearing, endowment, endogenous variable, exogenous variable, tax incidence, specific tax, per-unit tax, deadweight loss, DWL, consumer surplus, producer surplus, tax burden, elasticity and tax incidence, MRT, marginal rate of transformation, budget constraint slope, ECON 302, intermediate microeconomics