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Originally the consumer faces the budget line p1x1 + p2x2 = w. Then the price of...

Originally the consumer faces the budget line p1x1 + p2x2 = w. Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and wealth becomes 4 times larger.

a. Write down an equation for the new budget line in terms of the original prices and wealth.

b. Draw each budget constraint on a separate graph. Then label the vertical intercept, horizontal intercept and the slope of each line in terms of the original prices and wealth.

Note: Please show all steps in finding the slopes of the lines.

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Answer #1

a).

Consider the given problem here the equation of the budget line is given by, “P1*X1 + P2*X2 = W”, => if we measure the “X1” on the horizontal axis and “X2” on the vertical axis, => the horizontal and the vertical intercepts are given by, “W/P1” and “W/P2”. Now, the slope of the budget line is the ratio of “P1” to “P2” with negative sign, => “(-P1/P2)”.

Now, if “P1” get double, “P2” becomes 8 times larger and the wealth become 4 time larger, => the equation of the budget line is given by, => “2P1*X1 + 8P2*X2 = 4W”. If we measure the “X1” on the horizontal axis and “X2” on the vertical axis, => the horizontal and the vertical intercepts are given by, “4W/2P1 = 2W/P1” and “4W/8P2 = W/2P2”. Now, the slope of the budget line is the ratio of “2P1” to “8P2” with negative sign, => “(-2P1/8P2) = (-P1/4P2)”.

b).

Consider the following fig.

X2 AT W/P2 with slope l-P1/P2 81 W/P1 X1

So, here “A1B1” is the old budget line with slope “(-P1/P2)”.

X2 A2 W/2P2 with slope (-P1/4P2). 82 X1

So, here “A2B2” is the new budget line with slope “(-P1/4P2)”.

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