Answer to Question #271867 in Microeconomics for kalehiwot

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: U(x,y)=100 x^0.25 y^0.75

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:

$\frac{MU_x}{MU_y}=\frac{P_x}{P_y}=\frac{2}{5}$

and

$2x+5y=280.$

(b)

The computation of Lagrangian multiplier has a strategy of finding the local maxima and minima of a function subject to the 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.