Download Econ 188/288 Oct. 6, 2008 Shakeeb Khan Name: Fall 2008 Midterm

Econ 188/288
Shakeeb Khan
Fall 2008
Oct. 6, 2008
Name:
Midterm Exam
75 mins. Total of 75 points (points in parentheses).
1. (20) A firm’s total cost function is of the form:
T C = 100 + 4q + 4q 2
where q denotes number of units produced.
(a) Derive an expression for average cost.
(b) In which (if any) range of output is production characterized by
scale economies?
2. (30) The inverse market demand for fax paper is given by P = 400−2Q.
There are two firms who produce fax paper, each having marginal costs
of 40 per unit.
(a) Establish the Cournot-Nash equilibrium in this game.
(b) What are the firm’s profits in equilibrium?
(c) What is the monopoly output- i.e. the one that maximizes total
industry profit?
1
3. (25) Betty and Barney are friends. They will be playing a repeated game this
weekend. One round is played on Saturday and one round is played on Sunday.
The question is how will they use the afternoon. They can each choose between
'crash' (take a nap) and 'nosh' (have a beer and chips). Each day they make their
decision simultaneously. For either afternoon the game looks like
Barney
Betty
Crash
Nosh
Crash
0, 0
7, -2
Nosh
-2, 7
5, 5
The payoffs are in utility values, a sense of well being. If they both crash then they
both get a payoff of zero since they really haven't spent any quality time together. If
Betty chooses to crash and Barney chooses to Nosh then they payoffs are <7, 2>.
Betty's payoff is 7 because she didn't consume any unwanted calories and she got a
much needed rest. But if Barney is noshing while Betty is crashing his payoff is -2
since he is getting fatter and he feels as though he is being ignored by his friend.
a) What is the solution to the one shot game?
b) Now assume the game is played twice over the weekend and payoffs are
cumulated over the two stages of the game. What are (is) the nash equilibria of
the repeated game?
c) What is the subgame perfect equilibrium of the repeated game?
Note you are expected to justify all your answers.