ps1_sol0 - Solutions to Practice Problem Set 1 ECON 100C...

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1 Solutions to Practice Problem Set 1 ECON 100C Perloff Chapter 11 4. A monopoly has a constant marginal cost of production of $1 per unit and a fixed cost of $10. Draw the firm’s MC, AVC, and AC curves. Add a downward-sloping demand curve, and show the profit-maximizing quantity and price. Indicate the profit as an area on your diagram. Show the deadweight loss. Total cost (TC) is fixed cost plus variable cost (VC): TC = FC + VC = 10 + 1*Q. From total cost, we can derive the other cost functions: MC = TC/ Q = 1 AVC = VC/Q = 1 AC = TC/Q = 10/Q + 1 The profit-maximizing quantity Q* is determined where MR=MC. The marginal revenue curve will be downward sloping, and lie everywhere below the demand curve (since for a monopolist marginal revenue is less than the price). Note that the price P* that a monopoly firm charges is determined by the height of the demand curve at Q*. 5. Can a firm be a natural monopoly if it has a U-shaped average cost curve? Why or why not?
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2 Yes. As the ―Electric Power Utilities‖ application illustrates (p.383), the demand curve could cut the average cost curve only in its downward-sloping section. Consequently, the average cost curve is strictly downward sloping in the relevant region. 23. The inverse demand curve that a monopoly faces is P = 100 – Q. The firm’s cost curve is C(Q) = 5Q. What is the profit-maximizing solution? How does your answer change if C(Q) = 100 + 5Q? To find the profit maximizing quantity, we set marginal revenue equal to marginal cost. Remember that the price is then given from the inverse demand, so that the price is explicitly a function of the quantity chosen ( P(Q) ): * * ( )* (100 )* 100 2 5 : 2 5 47.5 52.5 TR P Q Q Q Q MR Q MC FOC MR Q Q P The answer does not change with the second cost function since MC and the demand curve (and hence MR) are the same as before.
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ps1_sol0 - Solutions to Practice Problem Set 1 ECON 100C...

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