A monopoly produces a good with a network externality at a constant marginal and average cost of

c$=$$$3$

$.$ In the first period, its inverse demand curve is $\backslash [$ p$=13-1$ Q $\backslash$text $\{.\}\backslash ]$ In the second period, its inverse demand curve is $\backslash [$ p$=13-1$ Q $\backslash ]$ unless it sells at least

Q$=9$

units in the first period. If it meets or exceeds this target, then the demand curve rotates out. by

$\backslash$alpha

$($it sells

$\backslash$alpha

times as many units for any given price$),$ so that its inverse demand curve is $\backslash [$ p$=13-\backslash$frac$\{1\}\{\backslash$alpha$\}$ Q $\backslash$text $\{.\}\backslash ]$ The monopoly knows that it can sell no output after the second period. The monopoly's objective is to maximize the sum of its profits over the two periods. For what values of

$\backslash$alpha

would the monopoly earn a higher two$-$period profit by setting a lower price in the first period? If

$\backslash$alpha

is $9.($round your answer to two decimal places$)$