All simulators
Constrained Optimum: Budget & Indifference
Utility maximisation on a budget line: tangency, the Lagrange multiplier and the cost of a non-optimal bundle.
Day 26: Constrained Optimisation & Lagrange Multipliersoptimum (x*, y*)
(15.0, 10.0)
x* = αM/pₓ
λ (shadow price)
0.1129
dU*/dM
candidate utility
9.40
optimum 11.29
MRS at candidate
0.082
price ratio 0.286
budget lineindifference curve through the optimumcandidate bundle
Maximise U = x^α y^(1−α) on the budget line. At the optimum the indifference curve is tangent to the budget line (MRS = pₓ/p_y), i.e. ∇U = λ∇g. The multiplier λ is the utility gained from one more dollar of income.