equilibrium effects

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. Consumers are named using real numbers, x, between 0 and 1. Each consumer is interested in buying at most one unit of a good. The reservation price that consumer x has for this good when fraction z of the population buys the good is given by r(x)f(z) where r(x)=1-x and f(z)=10z. Suppose that the price of the good is 0.9.There are two possible non-zero equilibrium fractions of the population purchasing the good.

a. The smallest non-zero equilibrium fraction of the population purchasing the good is: (Enter your answer in the format x/x)

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