Question

Consider the budget line 7x + 2y = 17.

(A) Read off the prices px, py and the consumer’s wealth m.

(B) If the consumer spends all his money on good 1, how many units can he afford? Likewise, if he spends all his money on good 2, how many units could he afford?

(C) Graph the budget set. What is the slope of the budget line?

(D) What is the definition of a numeraire good?  

(E) Express the budget line in an equivalent form that makes good 1 the numeraire.

(F) Express the budget line in an equivalent form that makes good 2 the numeraire.

(G) What does it mean for a particular bundle to be the numeraire? Say, if the bundle (4, 5) was numeraire, what would that mean, exactly?

(H) Express the budget line in an equivalent form so that the bundle (4, 5) is the numeraire. (Hint: you need to find prices px, py for which px py = 7 2 and 4px + 5py = 1.)

Answer 1

(A) The budget line is give by

Px*x+Py*y=m

7x+2y = 17

Px = 7

Py = 2

m = 17

(B) If teh consumer spends all income on x the y = 0

This means 7x = 17

x = 17/7

Likewise if x = 0, from Budget line:

2y = 17

y = 17/2

(c)

slope of the budget line is the price ratio:

= - Px/Py

= - 7/2

(D) Numeraire good is a representative base good and is priced at one unit.

(E) Good 1 as numeraire implies that Px= 1

To get this we divide by 7 on both sides of the Budget line:

7/7x + 2/7y = 17/7

x+(2/7)y = 17/7

(F) Budget Line:

7x + 2y = 17

=(7/2)x + y = 17/2

3.5x +y = 6.5

(G)