.Hailey lives in city A and consumes two goods, 1 and 2, with the following utility function, u, (1, 82, h) = Ar}a -h where A > 0 is a constant and h is the number of hours to work. The goods prices in city A are pf and p, and the wage rate wa. Suppose h is fixed. Use the Lagrangean method to derive the (a) Marshallian demand functions, taking h as given. (b) Now suppose Hailey can choose h. Solve for the optimal h. Then derive the Marshallian demand functions and the indirect utility function. Show that the Marshallian functions are homogeneous of degree zero in prices and wage rate. That is, x; (tpi, tp, twa) = x; (p, p, wa) , i = 1,2 for any t

.Hailey lives in city A and consumes two goods, 1 and 2, with the following utility function, u, (1, 82, h) = Ar}a -h where A > 0 is a constant and h is the number of hours to work. The goods prices in city A are pf and p, and the wage rate wa. Suppose h is fixed. Use the Lagrangean method to derive the (a) Marshallian demand functions, taking h as given. (b) Now suppose Hailey can choose h. Solve for the optimal h. Then derive the Marshallian demand functions and the indirect utility function. Show that the Marshallian functions are homogeneous of degree zero in prices and wage rate. That is, x; (tpi, tp, twa) = x; (p, p, wa) , i = 1,2 for any t

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. Hailey lives in city A and consumes two goods, 1 and 2, with the following utility
function,
u. (1, 2, h) = Ar}a -A
where A > 0 is a constant and h is the number of hours to work. The goods prices
in city A are pf and på, and the wage rate wa.
Suppose h is fixed. Use the Lagrangean method to derive the
(a)
Marshallian demand functions, taking h as given.
Now suppose Hailey can choose h. Solve for the optimal h. Then
derive the Marshallian demand functions and the indirect utility function.
Show that the Marshallian functions are homogeneous of degree zero
(b)
in prices and wage rate. That is,
a; (tp, tp, twa) = x; (p^, p%, wa) , i= 1,2
%3D
for any t > 0.

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