Practice Final Exam: ECON 100A
1. Consider a …rm with production function given by
1=8
f (x1 ; x2 ) = (x1 )
1=8
(x2 )
:
Assume the prices of inputs 1 and 2 are w1 = w2 = 1.
(a) Find the levels of the inputs that minimize the cost of producing y units of the good — the
conditional input demands. (10 points)
(b) What is the minimum cost of producing y units (i.e., C(y))? (5 points)
(c) Suppose the price of the good is p = 64. What is the optimal level of production of the …rm
(i.e., y )? (10 points)
2. A monopolist sells in two markets that have demand functions given by
D1 (p1 ) = 200
p1
and
D2 (p2 ) = 100
(1=3) p2
The marginal cost of production is constant at c = 60.
(a) Assume the …rm can charge di¤erent prices to each group. What are the equilibrium quantities
in markets 1 and 2? (15 points)
(b) Suppose the …rm can charge only one price. Thus, its market demand is D(p) = 300
Calculate the Deadweight Loss (DWL) of the monopoly. (10 points)
4
3 p:
3. There are two …rms in the market that compete in quantities (i.e., Cournot competition). The cost
of Firm 1 is C1 (Q1 ) = 120Q1 and the cost of Firm 2 is C2 (Q2 ) = 120Q2 . The market demand is
P (Q1 ; Q2 ) = 300
3(Q1 + Q2 )
(a) What is Firm 1’s pro…t-maximizing quantity if Firm 2 produces 50 units? (10 points)
(b) Find the equilibrium level of production of each …rm and the equilibrium market price. (15
points)
4. Consider a consumer with preferences over current and future consumption given by
U (c1 ; c2 ) = min
1
c1 ; c2
2
where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2. Let
us assume that p1 = p2 = 1 and r = 0:2.
(a) Suppose that m1 = 10 and m2 = 22. What are the optimal consumption levels in periods 1
and 2 (i.e., c1 and c2 )? (10 points)
(b) Is the consumer in part (a) a saver or a borrower? Why? (5 points)
(c) Suppose the consumer is asked to choose between two income vectors, A = (m01 ; m02 ) and
B = (m001 ; m002 ): You know that (c1 ; c2 ) = (20; 16) is in the budget line corresponding to the …rst
income vector (i.e., A), and (c1 ; c2 ) = (20; 36) is in the budget line of the second one (i.e., B).
What income vector will this consumer select (i.e., A or B)? Why? (10 points)
1