Question

1. Prove that two indifference curves cannot intersect. (Hint: use the transi-tivity axiom)

(Part II: Budget Constraint) Put meat on horizontal and potatoes on vertical axis.

1. (Day 1) Suppose your income is $10, the price of both meat and potatoes is $1. Find the budget constraint equation and draw the budget line. Specify the two intercepts and explain what they mean.

2. (Day 2) The prices of meat and potatoes are now $0.5 and $2, respectively. In addition, your income doubled. Find the two intercepts, and explain whether you are better or worse off compared to yesterday.

Answer 1

1) Two Indifference curves (IC) can't intersect each other. We can prove it in the following manner :

Both A and B lie on the same IC i.e. IC1 ==> A ~ B

Both A and C lie on IC2 ==> A~C

By property of transitivity we can say that if A~B AND A~C then B~C .

But as it is clear from the diagram , bundle B has more of both X and Y therefore it has to have a higher utility than bundle C. Therefore B and C can't be at a level of Indifference.

Hence two ICs can never intersect each other.

Day1)

Here Budget constraint is M (1) + P(1) = 10 where M and P are the units of meat and potatoes consumed respectively.

As shown in the diagram below, AB is the budget line.

We calculate the intercept by finding out how much of that commodity can be consumed if the consumer were to spend all of his income on that commodity.

Hence , X intercept is calculated as 10/1 = 10 i.e. assuming potatoe Consumption is 0 and all can be spent on meat.

And similarly y intercept can be calculated as 10/1 = 10 i.e. assuming meat Consumption is 0 and all is spent on potatoes.

Day2)

Here budget line is : (0.5)M + 2P = 20

As shown in the diagram above , AB' is the budget line here.

X intercept here is 20/0.5 = 40 and Y intercept is 20/2= 10.

Consumer will be better off here because when he is at budget line AB' , all the bundles at budget line AB are still affordable. He can consume the bundles he could Consume yesterday and more new bundles as well that lie above AB and below AB' . Therefore he is better off today.