Choice

Question 1

What is the equation for relative prices derived from the budget constraint?

Answer 1

change in consumption of good 2/change in consumption of good 1 = -p1/p2

Question 2

When we have given prices, what does the equation for relative prices tell us?

Answer 2

The opportunity cost of the goods: how much of one good we need to give up to have another unit of the other good

Question 3

What is the mathematical utility maximisation problem (UMP) for the consumer?

Answer 3

max u(x1,x2)

Question 4

How do we solve the UMP?

Answer 4

By subbing the constraint into the utility function and differentiating with respect to one of the goods

Question 5

What do you have to do after getting the first order condition to prove that the bundle is optimal?

Answer 5

You have to check for sufficiency. You do this by getting the second differential and seeing if its negative.

Question 6

What are the instant solutions for the demand functions of a Cobb Douglas utility function u(x1,x2) = (x1^a)(x2^b)?

Answer 6

x1 = (a/a+b)m/p1
x2 = (b/a+b)m/p2

Question 7

How do we solve the UMP for perfect substitutes?

Answer 7

Compare the gradients of linear indifference curves and the budget constraint giving:
(du/dx1)/(du/dx2) = p1/p2