A monopolist has a cost function of $c(y)=y$ so that its marginal costs are constant at $\$ 1$ per unit. It faces the following demand curve: $$D(p)=\left\{\begin{array}{ll} 0, & \text { if } p>20 \\ 100 / p & \text { if } p \leq 20 \end{array}\right.$$ (a) What is the profit-maximizing choice of output? (b) If the government could set a price ceiling on this monopolist in order to force it to act as a competitor, what price should they set? (c) What output would the monopolist produce if forced to behave as a competitor?
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