9. Consider the two-period diagrams below; the diagram to the left shows the pos
ID: 2821801 • Letter: 9
Question
9. Consider the two-period diagrams below; the diagram to the left shows the possible consumption patterns. A new positive NPV project allows the consumption set to shift to the right (as shown in the figure to the right) such that the value of y is $7; meaning that the new maximum possible consumption in period 2 is up from S101 to $108. Assuming you want to maximize your consumption in the current period, how much additional consumption does the project add to your maximum possible consumption today? Consumption next period Consumption next period Ay $101 $101 $73 Consumption todayExplanation / Answer
We can compare two period consumption patterns in following manner-
{Consumption today before shifting the pattern / Consumption next period before shifting the pattern} = {(Consumption today after shifting the pattern/ Consumption next period after shifting the pattern}
= {Consumption today before shifting the pattern / Consumption next period before shifting the pattern} = {(Consumption today before shifting the pattern + x / Consumption next period before shifting the pattern + y)}
Where, Consumption today before shifting the pattern = $73
Consumption next period before shifting the pattern = $101
Shift in Consumption today (additional consumption today), x =?
Shift in Consumption next period (additional consumption next period), y = $7
Therefore,
$73 / $101 = ($73 + x)/ ($101 + $7)
Or ($73 + x) = $108 *$73 / $101 = $78.06
Or x = $78.06 -$73 = $5.06
Therefore additional consumption the project add to your maximum possible consumption today is $5.06
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