ECON400 HW assignment 5 due December 8 in class Question 1.Pricing of Multiple Products -1 Demand Pr

ECON400
HW assignment 5 due December 8 in class
Question
1.Pricing of Multiple Products -1

Demand

Product 1

q1=a1-b1*p1+d1*p2

Product 2

q2=a2-b2*p2+d2*p1

Parameters

Values

a1

120

b1

2

d1

1

a2

120

b2

2

d2

1

1.
Find the profit-maximizing prices
(P1, P2) for Product 1 and Product 2 for a multi-product monopoly. Find the
associated monopoly profit.
2.
Find the equilibrium in the market
where Product 1 and Product 2 are sold by two independent firms (Firm 1 and
Firm 2).Find the associated profits ofFirm 1
and Firm 2.
3.
Compare the prices in 1. and 2.
Explain why a monopolist selling two products (Product 1 and Product 2) would charge
a higher or lower price than two independent firms selling these products.
4.
Is it profitable for Firm 1 and Firm
2 to merge to become amulti-product monopoly? Compare
the profits before and after the potential merger. Explain.
5.
Using Excel, draw best-response
functions for firms 1 and 2. Label the axes and the functions plotted. Cut and
paste the figure into the Word file.
Note: you can use an Excel file “Pricing of
Multiple Products” uploaded on Blackboard.
Question
2.Pricing of Multiple Products-2

Demand

Product 1

q1=a1-b1*p1+d1*p2

Product 2

q2=a2-b2*p2+d2*p1

Parameters

Values

a1

120

b1

2

d1

-1

a2

120

b2

2

d2

-1

1.
Find the profit-maximizing prices
(P1, P2) for Product 1 and Product 2 for a multi-product monopoly. Find the
associated monopoly profit.
2.
Find the equilibrium in the market
where Product 1 and Product 2 are sold by two independent firms (Firm 1 and
Firm 2).Find the associated profits ofFirm 1
and Firm 2.
3.
Compare the prices in 1. and 2.
Explain why a monopolist selling two products (Product 1 and Product 2) would charge
a higher or lower price than two independent firms selling these products.
4.
Is it profitable for Firm 1 and Firm
2 to merge to becomemulti-product monopoly? Compare
the profits before and after the potential merger. Explain.
5.
Using Excel, draw best-response
functions for firms 1 and 2. Label the axes and the functions plotted. Cut and
paste the figure into the Word file.
Note: you can use an Excel file “Pricing of
Multiple Products” uploaded on Blackboard.

Question
3. Contest
A manufacturer promises to give a prize to one
of two dealers who wins a sales contest. The value of the prize is V=10 to each
dealer. The dealers compete by spending sales effortxi. The probability of winning is of the
Tullock form: p1(x?,x?)= x?/(x?+x?) and p2(x?,x?)=
x?/(x?+x?). Dealers have the same constant marginal cost of effort, c=1.
1. Write down
firm 1’s expected payoff from participating in the sales contest.
2. Find the
best response of firm 1.
3. Are effort
levels strategic substitutes or complements? Explain.
4. By analogy,
write the best response of firm 2.
5. The firms
are symmetric in all respects. Using the symmetry, find the equilibrium sales
efforts, x? and x?.
6. What is the
extent of rent dissipation (that is, what fraction of the prize value V is
spent in rent-seeking efforts)?
7. Would
dealers choose to participate in the sales contest? What are their expected
equilibrium payoffs from participation in the contest?
8. Sketch the
best-response functions or use Excel to draw them. Mark the Nash equilibrium.

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