Question

in microeconomics do transitive preferences mean that they are also complete?

Answer 1

In microeconomics, preferences simply means an order which a persoin gives to alternatives he consumes on the basis of their relative utility. Utility simply refers to how much satisfaction we get from the consumption of that perticular commodity. Keeping price of the good, income of the consumer and the availability of the good, preferences are totally based on the indivudial's taste.

Now the concept of transitivity and completeness is way different.

Transitivity axiom simply states that if good A is weakly preferred to B and at the same time Good B is weakly preferred to Good C than it implies that A is weakly preferred to C which could be shown as:-

Hence we can say that an agent have transitive preference when her preference are internally consistant on the other hand preferenece is considered to be as complete if she can compare two objects on some perticular grounds.

For example lets take two cases to understand this:-

(A) Suppose that a consumer is going to between two cars. He will choose the car which is the fastest. The preference are complete here. Also given two cars x and y either x is faster or y is faster or they both may have same speed. This preference is also transitive as If car x is faster than y and car y is faster than car z than we can say that car x is faster than car z.

(B) Suppose that noe the consumer will choose the car if it is both faster and bigger. These prefernce are transitive. If car x is bigger and  faster than y and car y is bigger and faster than car z than we can say that car x is bigger and faster than car z. However the preferences are not complete this is because an SUV is though bigger than a BMW but it is slower than the BMW. Hence it is not clear that which acr will the agent prefer.

Hence we say that it is not necessary that every transitive preference is complete also. So the above given statement does'nt follow.