Microeconomics homework question-proving that a good is normal

[Mike s]

Hey,
I need help with the following question in microeconomics:
A consumer lives in a world of two goods: computers and money. Let x be the number of computers,the consumer can buy.
$x\epsilon [0,1,2,3]$
The consumer has the following preference relation: If the consumer has money and no computers, he is willing to spend at most half of his money on buying a single computer. If the consumer has 1 computer, he is willing to spend 1/3 of his money on buying a second computer. If the consumer has 2 computers, he is willing to spend 1/4 of his money on buying a third computer.

A. Explain why $(0,M)$~$(1,\frac{M}{2})$~$(2,\frac{M}{3})$~$(3,\frac{M}{4})$

B.Explain why the consumer's preference relation can be represented the following utility function $U(x,M)=(x+1)M$.

C.Prove that computer is not an inferior good

I have managed to solve A,B , however I need help in C.

 

[Asim Riaz]

A. The consumer's preference relation can be represented in this way because the consumer is willing to spend a certain portion of their money on an additional computer, depending on how many computers they already have. For example, if they have no computers they are willing to spend up to half of their money on buying a single computer, and if they have 1 computer they are willing to spend a third of their money on buying a second computer, and so on. B. The consumer's preference relation can be represented by this utility function because it shows that as the consumer buys more computers, the amount of money they are willing to spend on each successive computer decreases. This is what the utility function shows - as the number of computers (x) increases, the amount of money (M) decreases. Thus, the utility function U(x,M)=(x+1)M captures the consumer's preference relation.C. To prove that computers are not an inferior good, we need to show that the demand for computers is not sensitive to changes in the consumer's income. In other words, we need to show that as the consumer's income increases, the demand for computers does not decrease. This can be seen from the consumer's preference relation, since they are willing to spend a certain portion of their money on an additional computer regardless of their income level. Therefore, the demand for computers is not sensitive to changes in the consumer's income, and computers are not an inferior good.