Question

You are given a total of $240 to buy either good X or good Y, which are priced at $6 and $10, respectively. Draw a budget line that expresses all combinations of the two goods that can be purchased with this budget. What happens to the initial budget line if the budget is reduced by 25%? What happens if the price of X doubles? What happens if the price of Y falls to 8?

Answer 1

6X + 10 Y = 240

Rewriting this in slope intercept form

10y = -6x+240

y = -6/10x + 240/10

y = -.6x + 24

We know that x and y cannot be less than 0

The y intercept is 24 and the x intercept ( where y=0) is 40

To find the x intercept let y = 0

0 = -.6x + 24

-24 = -.6x

-24/.6 = -.6x/-/6

40 =x

If the budget is reduced by 25%, that means 240 is 25% less or 75% of the original value

75% of 240 = .75*240 or 180

6x+10y = 180

10y = -6x+180

y = -.6x+18

The y intercept is 18 and the x intercept is 30

If the price of x doubles

6 will become 12

12x+10y = 240

10y = -12x + 240

y = -1.2x +24

The y intercept is 24 and the x intercept is 20

If the price of y falls to 8

6x+8y = 240

8y = -6x+240

y = -6/8x + 240/8

y = -.75x + 30

The y intercept is 30 and the x intercept is 40