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\begin_body

\begin_layout Standard
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Prof.
 Marek Weretka's
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Econ 301 Intermediate Microeconomics 
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Problem Set 11
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\begin_layout Subsubsection*
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Problem 1 (Oligopolistic Industry) 
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Below you can find market shares of major beer producers in the USA in 2000.
 
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<lyxtabular version="3" rows="10" columns="2">
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<cell alignment="left" valignment="top" usebox="none">
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\begin_layout Plain Layout
Bud Light  
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\end_inset
</cell>
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\begin_layout Plain Layout
36.8%
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\end_inset
</cell>
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<row>
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\begin_layout Plain Layout
Coors Light
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\end_inset
</cell>
<cell alignment="center" valignment="top" usebox="none">
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\begin_layout Plain Layout
19.1%
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</cell>
</row>
<row>
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\begin_layout Plain Layout
Miller Lite  
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</cell>
<cell alignment="center" valignment="top" usebox="none">
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\begin_layout Plain Layout
18.5%
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</cell>
</row>
<row>
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Natural Light 
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</cell>
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9.2%
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</cell>
</row>
<row>
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Busch Light 
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</cell>
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6.1% 
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</cell>
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<row>
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Michelob Light 
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</cell>
<cell alignment="center" valignment="top" usebox="none">
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3.3%
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</cell>
</row>
<row>
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Keystone Light 
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</cell>
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2.6% 
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</cell>
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<row>
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Millwaukee's Best Light 
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</cell>
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2.3%
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</cell>
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<row>
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Old Milwaukee Light 
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</cell>
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0.8%
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</cell>
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<row>
<cell alignment="left" valignment="top" usebox="none">
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Miller Genuine Draft Light 
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</cell>
<cell alignment="center" valignment="top" usebox="none">
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0.7%
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</cell>
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</lyxtabular>

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\begin_layout Standard
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The total light beer sales in 2000 amounted to 87 million barrels.
 
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a) Find the concentration ratio (a "big four" index) for the beer industry
 in the USA.
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b) Is this industry perfectly competitive or oligopolistic (concentrated)?
 Why? 
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c) In your opinion how would Trade Commission react to a merger proposal
 by Bud Light and Coors Light? Why? 
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\begin_inset Formula $\vphantom{}$
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\begin_layout Subsubsection*
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Problem 2 (Aircraft Industry) 
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The jet aircraft industry is dominated by two major competitors: Airbus
 (A - based in Europe) and Boeing (B - based in the USA).
 Both companies have similar technology allowing each firm to produce a
 jet at a cost of $20 (in millions).
 Accordingly, their costs functions are given by:
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\begin_inset Formula $TC(y_{A})=20y_{A}$
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\begin_inset Formula $TC(y_{B})=20y_{B}$
\end_inset


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In order to simplify our analysis, we assume there are no fixed costs.
 The inverse demand function for jets by major airlines is estimated to
 be
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\begin_inset Formula $p(y)=200-y$
\end_inset


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a) Find analytically profit function 
\begin_inset Formula $π_{B}(y_{B})$
\end_inset

 for Boeing, given that the production of Airbus amounts to 
\begin_inset Formula $y_{A}=100$
\end_inset

 jets.
 In a graph with 
\begin_inset Formula $y_{B}$
\end_inset

 on the horizontal axis and 
\begin_inset Formula $π$
\end_inset

 on the vertical one, plot the profit function.
 
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b) Is the production 
\begin_inset Formula $y_{B}=100$
\end_inset

 jets Boeing's best response to 
\begin_inset Formula $y_{A}=100$
\end_inset

? Why or why not? Find the optimal level of production, given Airbus produces
 
\begin_inset Formula $y_{A}=100,y_{A}=50,$
\end_inset

 and 
\begin_inset Formula $y_{A}=0$
\end_inset

? Mark the three points in space 
\begin_inset Formula $(y_{A},y_{B})$
\end_inset

.
 
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c) Find analytically the best response function for Boeing 
\begin_inset Formula $R_{B}(y_{A})$
\end_inset

 and plot it in the graph from point b) .
 
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d) Find analytically the best response function for Airbus, 
\begin_inset Formula $R_{A}(y_{B})$
\end_inset

 and add it to your graph from point b) 
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\paragraph_spacing onehalf
e) Find analytically the market price of an aircraft, the level of individual
 and aggregate production in a Cournot-Nash equilibrium.
 Also find the level of profit of each individual firm.
 Show the equilibrium in your graph from b.
 
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f) What is the deadweight loss (
\begin_inset Formula $DWL$
\end_inset

) associated with oligopolistic trading by the two firms? 
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g) Suppose the two firms A and B form a cartel.
 What is the aggregate level of production, and profit per firm given collusion?
 Does collusion benefit the two producers? 
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h) Find a deadweight loss (
\begin_inset Formula $DWL$
\end_inset

) given collusion, and compare it to the one from f) .
 Which loss is greater, why? 
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i) Is the considered cartel sustainable if the interactions, as described
 above, are only in the short run? Why? How about if the market interactions
 are repeated? Why? 
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\begin_inset Formula $\vphantom{}$
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\begin_layout Subsubsection*
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Problem 3 (Accounting & Audit services in the USA) 
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There are 
\begin_inset Formula $N>2$
\end_inset

 auditing firms in the USA (N is a parameter).
 "Production" 
\begin_inset Formula $y^{i}$
\end_inset

 of a firm i is measured in auditors' hours and a cost function is given
 by
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\begin_inset Formula $TC(y^{i})=10y^{i}$
\end_inset


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You can think of $10 as an hourly wage paid to an auditor.
 Again we assume no fixed cost.
 The inverse demand for auditing in the USA is
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\begin_inset Formula $p(y)=1000-y$
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where y is an aggregate supply.
 
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\begin_layout Standard
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a) Find the level of aggregate production and market price in two extreme
 cases: monopoly (
\begin_inset Formula $N=1$
\end_inset

) and perfect competition (Hint: recall that in the case of perfect competition
 the secret of happiness is 
\begin_inset Formula $p=MC$
\end_inset

.)
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b) Plot the inverse demand function and mark the two points located on it
 - one for competitive interactions and one for monopoly.
 
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\begin_layout Standard
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c) Find analytically the level of production 
\begin_inset Formula $y^{i}$
\end_inset

 supplied by each auditing firm and aggregate 
\begin_inset Formula $y$
\end_inset

 number of hours, market price for one hour, 
\begin_inset Formula $p$
\end_inset

, the level of profit and the deadweight loss in the industry, all in the
 Cournot - Nash equilibrium.
 Find all variables as functions of N.
 
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d) Find the values of aggregate production y and p for N=2, 5 and 10.
 Mark the corresponding values on the graph from b) 
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e) In the graph with N on the horizontal axis and p on the vertical one,
 plot the equilibrium price.
 What can you say about the price limit, as N goes to infinity? 
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\paragraph_spacing onehalf
f) In the graph with N on the horizontal axis and y on the vertical one
 plot the equilibrium aggregate production.
 What can you say about the limit of aggregate production, as N goes to
 infinity? 
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\paragraph_spacing onehalf
g) In the graph with N on horizontal and 
\begin_inset Formula $DWL$
\end_inset

 on vertical one plot the equilibrium 
\begin_inset Formula $DWL$
\end_inset

.
 What can you say about the limit of aggregate production, as N goes to
 infinity? 
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\begin_layout Standard
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\begin_inset Formula $\vphantom{}$
\end_inset


\end_layout

\begin_layout Standard
\paragraph_spacing onehalf
\begin_inset Formula $\vphantom{}$
\end_inset


\end_layout

\begin_layout Subsubsection*
\paragraph_spacing onehalf
Problem 4 (Externality) 
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\begin_layout Standard
\paragraph_spacing onehalf
\begin_inset Formula $\vphantom{}$
\end_inset


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\begin_layout Standard
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a) Give four examples of market interactions with externalities: two positive
 and two negative ones.
 
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\begin_layout Standard
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b) In each of your examples is the outcome Pareto efficient or not? Why
 or why not ? (you can answer this question assuming that market is not
 regulated) 
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c) In each case explain how possibly we could change incentives of the agents
 so that they are closer to socially optimal outcome? 
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\begin_layout Standard
\paragraph_spacing onehalf
\begin_inset Formula $\vphantom{}$
\end_inset


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\begin_layout Subsubsection*
\paragraph_spacing onehalf
Problem 5 (Positive externality) 
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\begin_layout Standard
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In this problem we study market interactions with positive externalities.
 We consider a plant that manufactures dynamite 
\begin_inset Formula $d$
\end_inset

 and a nearby farm producing tomatoes 
\begin_inset Formula $t$
\end_inset

.
 The dynamite's production cost is:
\end_layout

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\align center
\begin_inset Formula $TC_{d}(d,x)=(1/2)d²+(x-2)²$
\end_inset


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\paragraph_spacing onehalf
where 
\begin_inset Formula $d$
\end_inset

 is the amount of dynamite produced and 
\begin_inset Formula $x$
\end_inset

 is the intensity of use of a nitrogen in the production process.
 The side product associated with use of the nitrogen is ammonia - a fertilizer
 that is released to the air.
 Such fertilizer promotes growth of tomatoes making the production on the
 farm cheaper.
 In particular the higher the intensity x the lower is the farmer's cost:
\end_layout

\begin_layout Standard
\paragraph_spacing onehalf
\align center
\begin_inset Formula $TC_{t}(t,x)=(1/2)t²+2t-xt$
\end_inset


\end_layout

\begin_layout Standard
\paragraph_spacing onehalf
The prices of tomatoes and dynamite are: 
\begin_inset Formula $p_{d}=p_{t}=$
\end_inset

$1 
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a) Is the market interaction associated with a positive or negative externality?
 
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\begin_layout Standard
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b) Find the level of production of dynamite 
\begin_inset Formula $d$
\end_inset

 and intensity 
\begin_inset Formula $x$
\end_inset

 that maximizes the profit of the dynamite manufacturer.
 What is the maximal level of profit? 
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\begin_layout Standard
\paragraph_spacing onehalf
c) What is the marginal benefit (negative of marginal cost) from using 
\begin_inset Formula $x$
\end_inset

 in optimum.
 Give one number and show it on the graph with 
\begin_inset Formula $x$
\end_inset

 is on the horizontal axis.
 Explain why this is a reasonable number.
 
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\paragraph_spacing onehalf
d) Given the intensity 
\begin_inset Formula $x$
\end_inset

 from a) find the optimal level of production of tomatoes 
\begin_inset Formula $t$
\end_inset

, and the profit of the farmer.
 
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\begin_layout Standard
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e) Find the joint profit of the dynamite manufacturer and the farmer.
 
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\begin_layout Standard
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f) Find the 
\shape italic
pareto efficient
\shape default
 level of production of 
\begin_inset Formula $d,t$
\end_inset

 and use of nitrogen 
\begin_inset Formula $x$
\end_inset

.
 Compare these values to the ones obtained in points b and d.
 
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\begin_layout Standard
\paragraph_spacing onehalf
g) Is the marginal benefit from using 
\begin_inset Formula $x$
\end_inset

 in f positive, zero, or negative? Why? 
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h) Economists say that the positive externality is associated with too little
 activity, compared to the efficient outcome.
 Are your findings in this problem confirming this statement?
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