1. Consider a single firm facing inverse demand function
p=100-10q
where q is the quantity of the good produced and p is the price for the good.
The firm has a linear cost function C(q)=10q.
Find the firm's profit-maximizing quantity, q*.
2. Suppose now two firms are facing inverse demand function
p = 100 - 10Q
where Q=q_1 + q _ 2 is the total quantity of the good produced and p is the price for the good.
Each firm has linear cost function C(q) = 10q .
Find the competitive equilibrium output, Q *
3. Compare the monopoly price in Q1, call it p^M, to the competitive equilibrium price in Q2, call it p^CE,
What is p^M - p^CE
4. Consider the alcohol consumption problem (e.g., Tadelis 1.4) and suppose your payoff is given by
v (a ; theta)= (theta*a) - c*a^2
where c > 0 is the cost of consuming amount a and theta belongs to [1,6] is your tolerance for alcohol.
Find your optimal consumption when theta is distributed uniformly on the interval [1,6].