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Prof.
 Marek Weretka's
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Econ 301 Intermediate Microeconomics 
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Problem Set 10
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Problem 1 (Monopoly and Price Discrimination) 
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Consider Microsoft Company from Problem Set 9 question 4.
 Microsoft's inverse demand for the new operating system is given by
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\begin_inset Formula $p(y)=100-y$
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a) (
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1st-degree price discrimination
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) Suppose that Microsoft can perfectly price discriminate among the consumers.
 What is Microsoft's profit if in that case? Is the allocation 
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pareto efficient
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? What is consumer surplus? 
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Let's get more realistic and assume that Microsoft can charge different
 prices on two segments of the market: individual buyers and firms.
 The demands on two segments are:
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\begin_inset Formula $y^{I}(p^{I})=50-(4/5)p^{I}$
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\begin_inset Formula $y^{F}(p^{F})=50-(1/5)p^{F}$
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b) Show that if Microsoft does not price discriminate, the aggregate inverse
 demand is as in part a).
 
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c) (
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3rd-degree price discrimination
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) Find the level of sales, price, profit and elasticity of demand for each
 segment of the market.
 
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d) Compare producer's and consumer's surplus in the three cases: uniform
 price (PS#9 Q4), perfect discrimination (PS#10 Q1 part a) and 3rd-degree
 price discrimination (PS#10 Q1 part c).
 
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\begin_inset Formula $\vphantom{}$
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Problem 2 (Demand elasticity) 
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Suppose the demand facing the monopolistic firm is given by
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\begin_inset Formula $y(p)=1-p$
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a) Plot the inverse demand function, indicating the corner points.
 
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b) Calculate the value of the demand elasticity for 
\begin_inset Formula $y=0,y=0.5$
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 and 
\begin_inset Formula $y=1$
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.
 
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c) Suppose the total cost is given by 
\begin_inset Formula $TC(y)=cy$
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 where 
\begin_inset Formula $c$
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 is some positive number (
\begin_inset Formula $c>0$
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).
 Show formally that the monopolist will chose a point on the elastic portion
 of the demand.
 (i.e.
 elasticiy = 
\begin_inset Formula $ε\in(-∞,-1)$
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.) 
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d) Find the markup over a marginal cost 
\begin_inset Formula $c$
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.
 
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