Budget Line: 1. A consumer can just afford two bundles of x and y: (x, y) = (15,

Question

Budget Line:

1. A consumer can just afford two bundles of x and y: (x, y) = (15,15) and (x,y) = (6,18). Use this information to find an equation that describes this consumer’s budget line. Please show the work to get the answer.

2. A consumer has a bundle (what we will later call an endowment) of (x, y) = (10,10), and she can exchange x for y and y for x in a free market. In this market she can exchange one x for two units of y, use this information to find an equation thatdescribe a consumers budget line. Please show the work to get the answer.

Explanation / Answer

1)

two points are given which are just affordable that means these points are on budget line so we can easily find out buget line equation using point-slope method

step1 : find out slope

slope=y2 - y1 / x2 - x1

=18-15 / 6-15 = 3/-9 = -1/3

now equation will be given by

y - y1 = slope (x- x1)

y- 15=-1/3 (x-15)

3y-45= 15-x

3y+x =60 is budget equation

2)

now one point on budget line is given (10,10)

and exchange rate between x and y is given, slope of budget will be equal to -2 , beacuse in order to get 2 more units of y , 1 unit of x needs to be sacrificed

so here budget line will be given by

y-10 = -2( x-10)

y+2x= 30

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