4. In an infinite period model, let y denote output and let ß = (1+r)¹. Let LATRI denote lifetime after-tax real income, where LATRI is defined as (for simplicity, all current and future taxes are 0): LATRI =y++By++1 + B²y++2 + Solve the right-hand side of LATRI by eliminating the future output variables in the following way: use the following equations for future output, where it is assumed that output grows by g percent each period (year); for example, g = 0.03, so that output grows by 3% per year: Y+1 (1g) y₁, Yt+2 = (1 + g) Yt+1, and so on. Use these equations, along with the rule for an infinite-period sum, to show that the equation for LATRI can be solved such that LATRI depends on current-period output y₁, as well as on r and g. Show your work. After deriving the equation for LATRI, do the following calculation. Assume that r equals 0.04, g equals 0.03, and y, is $40,000, and use the equation to calculate the dollar amount for LATRI (note that $40,000 x 1.04 equals $41,600). How many million dollars is LATRI equal to?
4. In an infinite period model, let y denote output and let ß = (1+r)¹. Let LATRI denote lifetime after-tax real income, where LATRI is defined as (for simplicity, all current and future taxes are 0): LATRI =y++By++1 + B²y++2 + Solve the right-hand side of LATRI by eliminating the future output variables in the following way: use the following equations for future output, where it is assumed that output grows by g percent each period (year); for example, g = 0.03, so that output grows by 3% per year: Y+1 (1g) y₁, Yt+2 = (1 + g) Yt+1, and so on. Use these equations, along with the rule for an infinite-period sum, to show that the equation for LATRI can be solved such that LATRI depends on current-period output y₁, as well as on r and g. Show your work. After deriving the equation for LATRI, do the following calculation. Assume that r equals 0.04, g equals 0.03, and y, is $40,000, and use the equation to calculate the dollar amount for LATRI (note that $40,000 x 1.04 equals $41,600). How many million dollars is LATRI equal to?
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.2P
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Transcribed Image Text:4. In an infinite period model, let y denote output and let ẞ = (1+r)¹. Let LATRI denote lifetime after-tax
real income, where LATRI is defined as (for simplicity, all current and future taxes are 0);
LATRI = y +By++1 + ß²y++2 + ...
Solve the right-hand side of LATRI by eliminating the future output variables in the following way: use
the following equations for future output, where it is assumed that output grows by g percent each period
(year); for example, g = 0.03, so that output grows by 3% per year:
=
Y+1(1+g) y₁,
=
Yt+2 (1+g) Yt+1,
and so on.
Use these equations, along with the rule for an infinite-period sum, to show that the equation for LATRI
can be solved such that LATRI depends on current-period output y₁, as well as on r and g. Show your
work. After deriving the equation for LATRI, do the following calculation. Assume that r equals 0.04, g
equals 0.03, and y, is $40,000, and use the equation to calculate the dollar amount for LATRI (note that
$40,000 x 1.04 equals $41,600). How many million dollars is LATRI equal to?
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