EconomicsLesson 2 of 5

Consumer Theory & Utility Maximization

Formulas

Marginal Rate of Substitution

MRS₁₂=MU₁ / MU₂=(∂U/∂x₁) / (∂U/∂x₂)

Rate at which the consumer is willing to exchange good 2 for good 1, holding utility constant.

Tangency Condition

MRS₁₂=p₁ / p₂

Equivalently: MU₁/p₁ = MU₂/p₂ — equal marginal utility per euro spent.

Part 1 of 1

The Utility Maximization Problem

The consumer picks the bundle (x₁, x₂) that maximises utility, given a budget:

maximize U(x₁, x₂) subject to p₁x₁+p₂x₂=I

This is exactly the Lagrange problem from the math section. The budget line is the constraint — it shows every affordable combination. The consumer wants the highest indifference curve that still touches it.

Worked example

1p_x=€2, p_y=€4, income I=€80.
2Budget line: 2x + 4y = 80.
3Feasible points include (40,0), (0,20), (20,10).
4The optimum is the point where the indifference curve touches the budget line from outside.

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