The Utility function is given by U(x, y) = x(y + 1) (a) Solve the problem to maximise the utility, constrained by the budget using Lagrange Multipliers. (b) Show that the solution found does actually maximise the utility function (amongst feasible x and y choices). (c) Calculate the optimal values for x*, y*, λ* and U*
The Utility function is given by U(x, y) = x(y + 1) (a) Solve the problem to maximise the utility, constrained by the budget using Lagrange Multipliers. (b) Show that the solution found does actually maximise the utility function (amongst feasible x and y choices). (c) Calculate the optimal values for x*, y*, λ* and U*
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question 1
Consider the budget constrained utility maximisation problem between two goods,
Good, and Goody.
Let x be the quantity of Good, whose price is $13 per unit and
y be the quantity of Good, whose price is $15 per unit
The total budget is $560. (Therefore, the budget constraint is 13x + 15y
The Utility function is given by U(x, y)
= x(y + 1)
=
560).
(a) Solve the problem to maximise the utility, constrained by the budget using Lagrange
Multipliers.
(b) Show that the solution found does actually maximise the utility function (amongst
feasible x and y choices).
(c) Calculate the optimal values for x*, y*, λ* and U*
(d) Consider now the dual optimisation problem of minimising the cost (Budget, B(x, y))
to achieve the utility U* as calculated in (c). Relate the optimal values of this problem
to those found in (c) and also B*.
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