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41. Consider a closed economy without government spending or taxes. The equilibrium
value of output in each period is determined by the equality of (the value of) output and
expenditure. Saving in period t is given by S(t) = s · Y (t) and investment expenditure in
period t + 1 is given by I (t + 1) = a + b · Y (t), for all values of t. a is a positive constant, s
and b are positive constants less than unity and Y(t) is the value of output in period t.
What relation must hold between the values of s and b for there to exist a value of
output in this economy, which once achieved in a time period will continue to persist in
subsequent periods of time?
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