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Suppose a monopolist producing Q units of output faces the demand curve P = 20 – Q. Its total cost when producing Q units of output is TC = F + Q2, where F is a fixed cost. The marginal cost is MC = 2Q.
a) For what values of F can a profit-maximizing firm charging a uniform price earn at least zero economic profit?
b) For what values of F can a profit-maximizing firm engaging in perfect first-degree price discrimination earn at least zero economic profit?
Answer : a)profit-maximizing firm charging a uniform price i,e at equilibrium , MR = MC Revenue = 20Q – Q^2 MR = 20 – 2Q MC = 2Q At equilibrium , 20 – 2Q = 2Q Q = 5 Revenue = 75 TC = F + 25 To earnat least zero economic profit : Revenue = TC Hence ,F + 25 = 75 F = 50 b) profit-maximizing firm charging a price using first degree…

ice discrimination, P = MC Revenue = 20Q – Q^2 MR = 20 – 2Q P = 20 – Q At equilibrium , 20 – Q = 2Q Q = 20/3 Revenue = 800/9 TC = F + 25 To earn at least zero economic profit : Revenue = TC Hence ,F + 25 = 800/9 F = 575/9

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