Question

1. Say that an individual's preferences for consumption (a composite of all the goods he likes) are expressed in functional form according to: Utility- U(C)a bC, where Cis consumption. a. Are the values of each parameter ("a" and "b") positive or negative? Base your answer on your intuition about individuals' preferences and knowledge of al (helpful to use a graph). What is the individual's marginal utility? Note: this is the derivative of the utility function with respect to C. Is marginal utility positive for all values of C? b. c.

Answer 1

A) for a utility function, MU should be positive,

& It should exhibit Diminishing MRS

MU: dU/dC = 2aC + b

dMU/dC = 2a

For Diminishing MU: dMU/dC < 0

So , a< 0

Then b should be positive

Bcoz for utility Maximization point

dMU/dC = 0

2aC + b = 0

C*= -b/2a

So C* should be positive, then for it, b should be positive, as a is already negative

a < 0 & b>0

a is negative

b is positive

.

B) MU = 2aC + b

c) MU> 0

Then, 2aC + b> 0

C > -b/2a

So for all C that is greater than (-b/2a), MU is positive