10. Determine if the following statement is either True or False. A consumer is indifferent between the original budget set and the budget set emerges when we decrease income by one-half and reduce each price by 75 percent. This question is worth 10 points.

Let original budget set be

$\small p_1x_1 + p_2x_2 = m$

If we now decrease income by one-half and reduce each price by 75%,

new income m' = m - 0.5*m = 0.5m

new prices:

$\small p_1' = p_1 - 75\%p_1 = p_1 - 0.75p_1 = 0.25p_1$

$\small p_2' = p_2- 75\%p_2 = p_2 - 0.75p_2 = 0.25p_2$

New budget constraint:

$\small p_1'x_1 + p_2'x_2 = m' \Rightarrow 0.25p_1x_1 + 0.25p_2x_2 = 0.5m \Rightarrow p_1x_1 + p_2x_2 = 2m$

Compared to original budget, income now doubles effectively if we assume prices same as earlier. Optimal consumption bundle will change because now consumer can reach to higher indifference curve and can have more utility.

Hence, the given statement is false.

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