HomeWork 4

HW: 10152012 (PART A)

Q1. PR-Corporation: $500 each unit, 6000 units/mth
       Competitor: $450 each unit
       Problem: Cuts PR-C's sale volume from 6000 to 4500

a. What is the arc price elasticity of demand between Potomac's oven and the competitor?

     4500 - 6000               -1500  =    $1050    
   4500   + 6000    =       -$150        10500   = 0.1 ~ 1.00(arce)
      $450 - $600                    
      $450 +$600         

b. Unit Elastic. Loss of sales may be a direct onsequence of decrease in consumer income.
c. -3.0 = 4500 - 6000  
               4500 + 6000 =      X = 454.54
               $X - $600
               $X +$600


Q2. -2.2 = .20 * X --> .20 * -2.2 = -44 --> take absolute value of -44. This leads to a percentage increase in the quantity of computers sold will be 44%

Q3.     1800 - 1500
        (1800 +1500)/2  =  300  *   2     = .001
          2.25 - 1.75            .50     1650
       (2.25 + 1.75)/2

Q7. 15 = (P) (1 + (1/1.2)) = 15 = (P)(.167) = 90, because 15/.167 equals 90 and 90 * .167 equals the
       marginal revenue.
Q8.

HomeWork 092412

Managerial Homework
Complete the following:
I.
Investment 1            Investment 2
    rj    pj                       rj    pj
-100    .05              -1000    .01
    0    .05                -500    .05
100    .05                     0    .53
200    .80                 500    .40
300    .05               1000    .01

Find  𝑟 for both investments

Investment1: (-100*.05) + (0*.05) + (100*.05) + (200*.80) +(300*.05) = 175
Investment2:(-1000*.01) + (-500*.05) + (0*.53) + (500*.40) + (1000*.01) = 175


Find σ for both investments
Invest.1: SQRT( (-100-175)^2 + (0-175)^2 + (100-175)^2 + (200-175)^2 +(300-175)^2) =  80.039
Invest.2: SQRT( (-1000-175)^2 + (-500-175)^2 + (0-175)^2 + (500-175)^2 +(1000-175)^2) = 319.2

I1. 175/80.039= 2.18 ** more risky
I2. 175/319.18=.55


II.
Assume you face an investment such that 𝑟=1000 and σ=300
What is the probability that this investment makes less than 0? 300? 1000? 1500?


1.  0-1000/300 ---> -3.33; P = .0004
2. 300-1000/300----> 2.33; P = .9901
3. 1000-1000/300---> 0; P = .5000
4. 1500-1000/300---> 1.64; P = .9495

Homework 091012

Problem 1:

Total Cost: 300 +  75q + 5q^2
Price: 825 - 20q

#1.  Profit = (825 -20q) q - 300 - 75q - 10q
       P = 825Q - 20Q^2 - 75 - 10Q
       P = 825 - 40Q - 75 - 10Q     
       P  = 750 - 30q

#2. Thus,

      dTR = 750/30q  = 25q**
       dQ

#3. Price:   825 - 20(25) = 325

      Min: 25; Max: 30

#4. TR= (825 - 20(25)) (25)
      = 325 * 25
      = 8 ,125

#5. TC=  75Q + 5Q^2
           =  75(25) + 10(25)
           = 2,125

#6. Profit =6000


Problem 2:
TC = 34 + 80Q + 12Q^2
 P = 160 + 2Q

Profit =160q + 2q^2 - 34 - 80q- 24q
      P= 160q + 4q - 80q -24q
      P = 80 - 20q (1st "D")

Thus,

dTR= 80-20q = 4
dQ

Price=  P = 160 + 2(4) = 168

Min: 4; Max: 20


TR= (160 + 2(4)) (4) = 672

TC =  80(4) +24(4) = 416

Profit = 256