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

a) What is the restrictions on the value of $\alpha$ such that this person is an ordinary and rational consumer? Why?

b) Given those restrictions on $\alpha$ , derive the Marshallian demand functions of the consumer.

c) What is elasticity of substitution? Explain in your own words the concept of elasticity of substitution.

d) Calculate and interpret the elasticity of substitution in this case.

Answer 1

@ the resmiction for being the ordinary and Rational Consumer is os & al. if & to then no rational consumes will buy it as the marginal ability derived from a becomes negative. (this is rutionalin - if &71 that means the law of diminishing manginal Returns violates and we cannot de termine the factor shame as well, so, & 81 implies ordinany consumer

1. The Marshallion dd fy will be : - the Shontent without using lagnan giun! u (122) = a,& xl , sit. Pid, then = y. & 2* - xy = (1-d) d P this is the Standard Formula ose lastbility of sw, wahin substith hon Where dln(MRS) 1 MRS = manginal Rute of substitution MRS -masin mas means for a unit sacrifice in a how much to you will get a and elasticity of substitution means as per unit Change of mRS changes, how the relative demand Carve for (21 de) Changes. P - Calculate: calculation and mosan :) a los amante

Now 1. Cremembes, las The intuition of this is cobb-doglus in is a CRS (constant Returns to scale) fr ay f(222). 2 2,214 and il why =ta,a na elasticity of substitution is 1.