Question

3. There are two goods x and y. Milton preferences for bundles of x and y can be described as follows: Between any two bundles, Milton prefers the bundle that has more x. If two bundles have the same amount of x, he prefers the bundle that has more y. (Obviously, bundles with the same amount of x and y are the same bundle).

a. Prove that Milton’s preferences satisfy the completeness assumption. (6)

b. Describe what the indifference curves look like. (2)

Answer 1

(A) Milton's preferences satisfy the completeness assumptions are as under:

Economists believe that buyers are motivated by a collection of expectations they use when deciding between goods. Three properties will satisfy certain preferences: completeness, transitivity and "more is better."

1.Completeness

If consumers are presented with a choice between any two bundles of products, they will rate them. Which excludes the risk which customers would not be able to determine which package is preferable. Completeness allows the consumer to be able to list all applicable states around the world, where a state is applicable because the consumer may theoretically select it. It is clearly a huge problem, since usually there are a large number of variables influencing a decision issue, so the number of states that a customer may consider is high.

In reality, customers use heuristics and approximations to solve their problem of decision; they do not, of course, solve the formal, fully-specified problem of optimization. Nonetheless, this modeling method is useful because it provides a reasonable approximation of consumer behavior, while also offering a good balance between tractability and empirical relevance.In addition, market demand and preference models based on this simple framework generally do very well to explain behaviour, indicating that this particular simplification of modeling is quite useful.

For a basic question of consumption where the user has to choose between consuming an orange and a mango two world states will be "I have an orange " and "I have a mango ."There the preferences over states collapse down to simple preferences over goods and we see that simple preferences described over bundles of goods are actually just a particular case of the more general notion of preferences over world states.

2.Transitivity

Transitivity of expectations is a central concept shared by most of the major logical, prescriptive, and concise decision-making models of today. An individual, group or society that prefers choosing choices to y and y to z must prefer to z to have transitive preferences. Any argument by individual decision-makers for empirical transitivity violations needs proof beyond a fair doubt. Normal transitive preferences operationalizations and discussion of systemic methodological problems in the collection, modeling, and study of applicable empirical evidence. For example, violations of weak stochastic transitivity do not mean breaches of preferential transitivity.

Based on past multidisciplinary research, we use parsimonious mixture models, where the family of (transitive) strict linear orders is the space of permissible preference states.

3. 'More is better' is the third properties to satisfy the preferences which the consumer have and choose it from the various option available to him to satisfy his wants.

(B) Indifference curve

An indifference curve shows the different combinations of two products that offer equal utility or satisfaction to the user. A higher curve of indifference corresponds to a higher degree of happiness, whereas a lower curve of indifference corresponds to less contentment. We have no hint, however, of how much additional pleasure or benefit a higher curve of indifference suggests. A calendar of indifference showing the different combinations of hamburgers (good X) and soft drinks (good Y) which offer the customer equal satisfaction.

Indifference Schedule Hamburgers (x) Soft Drinks (y) Combinations

1014 Soft drinks (Y) per unit of time 6 3 1 0 12 4 7 Hamburgers (X) per unit of time

Individuals are indifferent to combinations A, B, C and F since they all lie on indifference curve U1