In infinite-period analysis the following condition describes the nominal price of a share of stock in period t:
For all of the subsequent analysis suppose that the utility function in every time period is
1. Consider the following two scenarios:
Scenario 1. Suppose that at the start of period t everyone (that is markets) knows exactly what the numerical values of all prices and quantities (and inflation rates and dividends) are on the right-hand-side of the expression above.
Scenario 2. Suppose that at the start of period t everyone knows exactly what the numerical values of all prices and quantities (and inflation rates and dividends) are on the right-hand-side of the expression above and that all of these prices and quantities (and inflation rates and dividends) on the right-hand-side of the expression above are exactly the same as in Scenario 1 with the exception of nominal dividend payments during period t+1. Under Scenario 2 everyone (markets) believes that nominal dividend payments during period t+1 will be smaller than they believe under Scenario 1.
Thus Dt+1 under Scenario 2 is
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