How the Optimal Consumption Level of Goods Are Determined

This essay is to provide a concrete application of utility theory on to consumer behaviours. The first part of this essay will explains how the optimal choice of goods are determined with regards to utility theory, the last part will focus on how to derive the individual demand curve for a goods from indifference curve analysis.

Utility is arbitrarily assigned numbers used to rank options, this purpose of doing this to assist preference ranking, so that behaviours can be predicted. It is important to point out that utility is nothing to do with satisfaction or any psychological unit

(Stigler.G 1946).Also the ranking is, generally speaking, ordinal measure which means the differences between utilities cannot be compared.

There are some basic assumptions in utility theory to make it useful in explaining human behaviours. First, it is assumed consumer maximize their utility. Second, a consumer can tell his or her preference, this is the completeness assumption. The third assumption is transitivity assumption which means preferences are such that if good x is preferred to good y and good y is preferred to good z, then good x is preferred to good z. The forth assumption is non-satiation, which means a bundle with more of either good is always preferred to a bundle with less. The fifth is the postulate of substitution, this postulate assumes everything is exchangeable .If one said he is not willing to sacrifice any good x for any amount of all other goods, then his indifference curve for good x can not be drawn. The last assumption is the postulate of diminishing marginal rate of substitution. Marginal rate of substitution (MRS) of a good is the maximum quantity of other goods one is willing to forsake for obtaining one additional unit of that good, holding utility level constant. MRS is diminishing when moving along the same indifference curve. For goods which are perfect substitutes and perfect complements, MRS will be constant and zero/infinite respectively but these extreme cases will not be discussed in this essay although the optimal choice in these cases will also be the point that lies on the budget line and just touch the highest indifference cure.

Given the assumptions, a curve which is downward sloping and convex to the origin can be derived. This is the indifference curve, this is a graphical way to depict a consumer's preference, it is showing the set of all bundles of goods among which a consumer is indifferent. For the sake of simplicity, it is assumed a consumer only consume good x and good y only. Thus the indifference curve is now showing all bundles of good x and good y which is indifferent to a consumer. After knowing the consumer's preference, the constraints have to be set up. Again, for the sake of simplicity, it is assumed the consumer is a price taker. The constraint is the money he has. If he uses all his money to buy good x or good y, he got either 30 good x or 10 good y .Because he is a price taker, the line joining this two points is a straight line showing the price ratio (px/py).This line represents his budget constraint which means he cannot but bundles which lie on the right hand side of this line. For the bundles lie below this line, they are achievable yet they will not be chosen as a consumer always wants more. With ranking of options and the costs of obtaining each and every option, we can predict what a consumer will choose. The optimal choice will be the point that lies on the budget line and just touch the highest indifference cure.

Below are two graphical expression of the optimal consumption choice:

According to Fig 1 ,BL is the budget constraint ,U0,U1 and U2 represent different utility level. Point a and c are achievable yet total utility is not maximized. Point b is not achievable at current income level. Point e is the equilibrium bundle, as at point e, total utility is maximized with respect to the budget constraint, MRS(of y to x) is equal to the slope of budget line Price x/Price y. Moreover, an optimal choice that includes the consumption of both goods(X1,Y1) is called the

interior solution.

Fig 1

In