# Consumer Theory Mathematical Notation

Please open the attached word file to view the mathematical notations.

Question

Consider a consumer with utility function

(a) Find the demand for any vector of strictly positive prices, p = (p1,p2)>>0 and any level of income, M>0,. Why does the consumer end up spending her entire income (i.e., choose a consumption point on the budget line)?

(b) Sketch some indifference curves of the utility function u and draw the price consumption curve (PCC), which results when varying the price of the first good. Does the first good have a normal price effect, and how does this show in the PCC?

(c) Is the following statement true or false: A normal good (a good with positive income effect) cannot be a Giffen good. Explain briefly why you arrive at your conclusion.

https://brainmass.com/economics/utility-demand/consumer-theory-mathematical-notation-182559

#### Solution Preview

Please see the attached file.

Question: Consider a consumer with utility function .

(a) Find the demand for any vector of strictly positive prices, p = (p1, p2)>>0 and any level of income, M > 0. Why does the consumer end up spending her entire income (i.e., choose a consumption point on the budget line)?

MUx1 =

MUx2 =

MRS = MUx1/MUx2 = / = x2/x1

The utility is maximized where MRS = MUx1/MUx2 = p1/p2,

Or p1x1 = p2x2

The budget line is given as: p1x1 + p2x2 = 1

Plugging in p1x1 = p2x2in the budget line, 2p1x1= 1, which gives ...

#### Solution Summary

The consumer theory mathematical notation are determined.