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