1
ECON 815: Economic Analysis for Business
Solutions for Problem Set 2
Professor D. Weisman
2
1.
Q  4 K 0.5 L0.5 and r  2, w  2
a) As per class discussion, observe that exponents are the same(0.5) for K and L and prices for inputs
are the same, so that K = L.
(1)
32  4 K 0.5 K 0.5  4 K  K  8, L  8
b) CRS: The sum of the exponents is 0.5+0.5 = 1
Technology 1
2.
 1 
Q  min  K , L 
 2 
Technology 2
and
Q
1
1
K  L . r  2, w  1
2
4
a) Technology 1 requires 1K and 2L per unit
(1)
C  Q   1 2  2 1  4Q
Technology 2. Compute and compare
MPK  MPL
r  W
1
MPK 2 1 MPL
  
 use either
r
2 4
w
K or L to produce output since equally efficient per unit.
Suppose use L
(2)
C  Q    4 1  4Q . Note: costs are the same at current input prices.
b) Recommendation: Technology 2, Q 
1
1
K L
2
4
Why?
Costs are the same at current input prices, but input prices can change.
The perfect substitutes technology enables the firm to vary its input mix in the face of changing input
prices. Technology 1 does not allow for this flexibility and thus renders the firm more vulnerable to input
price volatility.
3. The “or” indicates perfect substitutes. Hence,
(1) Q  2 K  1L
Constant Returns To Scale: CRS
(2)
Q'  2  2K   1 2L  2  2K  1L  2Q
The firm will use only capital when
(3)
MPK MP
2 1

   r  2w
r
w
r w
3
4.
Q  n  min K , L
a) Each unit of output requires :
r
1
1
K and L
n
n
r  w
Q
n 
w
(1) C  Q      Q  
n n 

No. Why? Mergers result in n becoming smaller 
1
is growing larger. Hence, mergers lead to lower
n
efficiency in production and hence higher costs.
Note:
(2)
C  Q 
 r  w Q  0

n
n2
Increasing n lowers costs and thus decreasing n (upon allowing mergers) raises costs.
5. Technology A:
Technology B:
I A  300 and Q  2K  L
I B  400 and Q  x min 2K , L
a) r = $12 and w = $2
Technology A:
MPK
2 1 1 MPL

  
 Use only L
r
12 6 2
w
Each unit of output requires 1 unit of labor
(1)
C  Q   1 2 Q  2Q
Technology B: Each unit of output requires
1
1
K and L .
2x
x
 12 2 
6  2
8
 Q  
Q   Q

 2x x 
 x 
x
(2) C  Q   
b) The firm is rational and hence cost-minimizing.
Let Q=100. If firm will chooses Technology B, then
Costs with Tech. B
Costs with Tech. A
8
(3) 400+
 x  100  300+2 100 
8
8
(3’)   100  100   1  x  8
x
x