The local cement market is a duopoly with City Cement and Mountain Cement producing quantities q c

Question:

The local cement market is a duopoly with City Cement and Mountain Cement producing quantities

q_{c}

and

q_{m} .

Cement is a homogeneous product with the inverse demand function

p = 20 ˆ’ Q,

where

Q = q_{c} + q_{m} .

Each firm has a marginal cost of $4 and a fixed cost of $6. City Cement is a Stackelberg leader that sets output first. Mountain Cement acts as a follower. Mountain€™s best response to any output of City€™s is

q_{m} = 8 ˆ’ q_{c} / 2.

a. Create a spreadsheet with columns for $q_{c}, q_{m}, Q, p,$ and the revenue and profit of each firm. Let $q_{c}$ take on the values of 0 to 16 in increments of 2 and use the spreadsheet to determine the other values in the table. Assuming that Mountain cannot avoid its fixed costs by shutting down, what output level will City Cement choose?

b. Now use the spreadsheet to determine the monopoly output by setting $q_{m} = 0$ no matter what output City produces. What is the monopoly price and output? How do these amounts compare with the industry price and output for the Stackelberg model?