Question

A consumer with convex, monotonic preferences consumes non-negative amount of $x_{1}$ and $x_{2}$ . This consumer faces the budget constraint and has the utility function

where

a) Derive the indirect utility function.

b) Derive the expenditure function.

c) Explain briefly according to your understanding the link between direct, indirect and expediture function.

Answer 1

Answer - sep, + 2 Pz eg dan Ulm, 1912) = 21 9 4 3 - @ LE **, -a +1 (4- PI = 547 Pr ) of a certain na - MPI = 0 0 John 6-c) mchele - 1P=0 ☺ OL = m. Put Me Pz = y — ☺ from 0 and ② , we get, Jx (3-d) het di 12 md P (1-2d), and z fz From ② , apit (1-2) Il fz R 1 =4 adrip, + (1-22)P, 21=axy 24A + Pixi-adhili zady 2a 1, *=(-23) y 2x) y - Pz function can be of sit & na into Indirect utility the values forend by putting original Wility

U pour () 7" - (Just courtya [el-model gegee Indirect utility function. Now to deritve the expenditure function, we know that , my income will be my expenditure, from Iuf , (4) . u= 124 ya ya ( (1-203 72-a yž - * - 109 ) ( Sarayda g' P yde det er en | yle.hr) - 2 ) ( 24 - d 19 expenditure function.