Description

Exercise 1: Differentiated Products

Consider two firms with linked products and have unit marginal cost (c = 1). The inverse demand function for each firm is as follow:

p1(q1, q2) = 9 − q1 − dq2

p2(q1, q2) = 9 − q2 − dq1

1. Write the profit function of each firm

2.  For which value of d that the two goods are complements, perfect substitutes, imperfect substitutes and independent? Compute the demand function in each case.

3. Compute and draw the best response function of each firm when firms set prices for d = 0, and 1. Are prices strategic substitutes or complements? Compute and draw the equilibrium prices. What is the impact of an increase in product substitutability?

4. Compute and draw the best response function of each firm when firms set their own quantities for d = 0,  and 1. Are prices strategic substitutes or complements? Compute and draw the equilibrium prices. What is the impact of an increase in product substitutability?

5. What is the first best output, which maximizes social welfare knowing that the utility function for a representative consumer for these two goods is as follow:

U(qo,q1,q2)=q0 +9q1 +9q2 –

Compare with the above values.

Exercise 2: Price and Quantity Competition

1. (4 points) Consider a market with two firms producing two differentiated products with unit marginal cost (c=1) and inverse demand functions as in Exercise 1:

p1(q1, q2) = 9 − q1 − dq2

p2(q1, q2) = 9 − q2 − dq1

Show that profits under quantity competition are higher than under price competition if products are substitutes and that the reverse holds if products are complements.

Exercise 3: Industries with Price or Quantity Competition

1. Which model, the Cournot or the Bertrand model, would you think provides a better approximation to each of the following industries/markets: the oil refining industry, farmer markets, cleaning services and music industry. Discuss.

Exercise 4: Hotelling Competition

Suppose there are two street vendors selling hot-dog from a mobile cart in the street A. This street has nine blocks, each block has ten households living inside. We assume that each household consume only one hot-dog from one vendor, and their willingness to pay is equal to $10 minus the transportation cost of walking down to the street to the vendor to buy hot-dog. Assume that if households buy hot-dog in the same block, there is no transport cost, and for each block that they need to pass, it costs them 50 cents. Heavy regulations require that street vendors obtain licenses from Town Hall each morning. The cost of producing one hot-dog for each vendor is equal to 3$. Assuming that if consumers are indifferent between two vendors, each vendor get half of the demand.

1. Location choice
The Mayor Town provides licenses to two street vendors and sets the price to $ 7 per hot-dog. Although the Town Hall set price, vendors may choose their block locations. Suppose you are the owner of the vendor 1. What is the location of the block that generate the highest profits for your business regardless of the choice of vendor 2?

2. Price choice
Now, the City dramatically changes its policy; each vendor is assigned a location and can only operate in that location, but they are free to set their own price. Vendors are assigned locations at the extremes (one vendor in block 1, and one vendor in block 9). What is the equilibrium price and profit for each vendor?