1.-Dayna’s Doorstops, INC. (DD) is a monopolist in the doorstop industry. Its total cost function C(⋅) is given by the quadratic function of output C(Q) =100 – 5Q + Q2 . The inverse demand function for doorstops P(⋅) is given by the linear function P(Q) = 55 – 2Q . Note that the marginal cost C′(Q) is not constant. (Also, it happens to be negative for 0 ≤ Q < 2.5.) (a) Write down the profit-maximizing problem for DD, and determine its optimal output, QM. (b) Find the profit-maximizing price set by DD, PM and its marginal cost at the output level QM. From these two pieces of information, can you compute the elasticity of demand at that same level of output without taking any derivative? (c) How much consumer surplus CSM and producer surplus PSM and total surplus does DD generate by its profit-maximizing plan? (d) Find the profit-maximizing output, Qc, if DD acted like a price-taker (i.e., a perfect competitor). (e) Find the profit-maximizing price set by DD, Pc, as well as its profit, πc, if it acted like a pricetaker. (f) Compute the deadweight loss resulting from the market power exercised by DD. 2.-Consider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is C(Q) = 6Q - Q^2/400 . (a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints). (b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.
1.-Dayna’s Doorstops, INC. (DD) is a monopolist in the doorstop industry. Its total cost function C(⋅) is given by the quadratic function of output C(Q) =100 – 5Q + Q2 . The inverse demand function for doorstops P(⋅) is given by the linear function P(Q) = 55 – 2Q . Note that the marginal cost C′(Q) is not constant. (Also, it happens to be negative for 0 ≤ Q < 2.5.)
(a) Write down the profit-maximizing problem for DD, and determine its optimal output, QM.
(b) Find the profit-maximizing
(c) How much
(d) Find the profit-maximizing output, Qc, if DD acted like a price-taker (i.e., a perfect competitor).
(e) Find the profit-maximizing price set by DD, Pc, as well as its profit, πc, if it acted like a pricetaker.
(f) Compute the
2.-Consider a market with 190 consumers. Of these, 90 of them have individual (inverse) demands given by: PM(Q)=10−Q, while each of the other 100 has an individual (inverse) demand of PS(Q)=10−10Q. The cost function of the monopolist serving this market is
C(Q) = 6Q - Q^2/400 .
(a) Find the aggregate demand. Analyze the cost function and find what kind of returns to scale it exhibits. Compute the efficient total output (ignoring break-even constraints).
(b) Compute the optimal linear price (and quantity) for this monopolist, and the deadweight loss.
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