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

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 â€œPricing of

Multiple Productsâ€ 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 â€œPricing of

Multiple Productsâ€ 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.