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# Consumer Theory Mathematical Notation

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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

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.

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