Answer to Question #267516 in Economics for RAHEL

Question

1.     A consumer has 280 to spend on two commodities, the first of which costs 2 per unit and the second 5 per unit. Suppose that the utility derived by the consumer from x units of the first commodity and y units of the second commodity is given by the  Cobb-Douglas utility functions as:

a)   How many units of each commodity should the consumer buy to maximize utility?

b)   Compute the Lagrange multiplier and interpret in economic terms?

Answer 1

a) The consumer should buy such quantities to maximize utility, for which:

$MUx/MUy = Px/Py = 2/5$ and 2x + 5y = 280.

b) The method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).