An appliance dealer must decide how many (if any) new microwave ovens to order for next month. The ovens cost $220 and sell for $300. Because the oven company is coming out with a new product line in two months, any ovens not sold next month will have to be sold at the dealers half price clearance sale. Additionally, the appliance dealer feels he suffers a loss of $25 for every oven demanded when he is out of stock. On the basis of past months sales data, the dealer estimates the probabilities of monthly demand (D) for 0, 1, 2, or 3 ovens to be .3, .4, .2, and .1, respectively. The dealer is considering conducting a telephone survey on the customers atti- tudes towards microwave ovens.

The results of the survey will either be favorable (F), unfavorable (U) or no opinion (N). The dealers probability estimates for the survey results based on the number of units demanded are:

P ( F I D = 0) = : 1
P ( F I D = 2) = : 3
P ( U I D = 0) = : 8
P ( U I D = 2) = : 1
P ( F I D = 1) = : 2
P ( F I D = 3) = : 9
P ( U I D = 1) = : 3
P ( U I D = 3) = : 1

a. What is the dealers optimal decision without conducting the survey?
b. What is the EVPI?
c. Based on the survey results what is the optimal decision strategy for the dealer?
d. What is the maximum amount he should pay for this survey?

Explanation:

Order 0: we have unsold items for which the return is -25

return is -25*(.4*1+.2*2+.1*3) = -25*1.1 = $-27.50

Order 1: we have to sell at a discount if no orders, otherwise sell 1, and unsold items if demand 2 or 3

return is .3*(1/2*300-220) + (1-.3)*(300-220) + -.25*(.2*1+.1*2) = .3*-70+.7*80+-25*(.4) =

-21 + 56 - 10 = $25

Order 2: we have to sell at a discount if 0 or 1 orders, sell 1 or 2, and unsold items if demand 3

return is (.3*2+.4*1)*(1/2*300-220)+(.4*1+(.2+.1)*2)*(300-220)+-25*.1 =1*-70+1*80-25*.1 =

-70 + 80 - 2.5 = $7.50

Order 3:

return is (.3*3+.4*2+.2*1)*(1/2*300-220)+(.4*1+.2*2+.1*3)*(300-220) = 1.9*-70 + 1.1*80 =

-133 + 88 = -$45

Order 1, with a return of $25, as this is the highest return.

b) If we had a perfect information, we would never pay a penalty for underordering or suffer a discounted return from over-ordering

(.4*1+.2*2+.1*3)*(300-220) = 1.1*80 = $88

Then, the value of perfect information is $88 - $25 = $63

c) P(D=0|F) = P(F|D=0)*P(D=0)/(P(F|D=0)*P(D=0)+P(F|D=1)*P(D=1)+P(F|D=2)*P(D=2)+P(F|D=3)*P(D=3))=

.1*.3/(.1*.3+.2*.4+.3*.2+.9*.1)=.03/.26 = 3/26

P(D=1|F) = P(F|D=1)*P(D=1)/(P(F|D=0)*P(D=0)+P(F|D=1)*P(D=1)+P(F|D=2)*P(D=2)+P(F|D=3)*P(D=3))=

.2.4/(.1*.3+.2*.4+.3*.2+.9*.1)=.08/.26 = 4/13

P(D=2|F) = P(F|D=2)*P(D=2)/(P(F|D=0)*P(D=0)+P(F|D=1)*P(D=1)+P(F|D=2)*P(D=2)+P(F|D=3)*P(D=3))=

.3*.2/(.1*.3+.2*.4+.3*.2+.9*.1)=.06/.26 = 3/13

P(D=3|F) = P(F|D=3)*P(D=3)/(P(F|D=0)*P(D=0)+P(F|D=1)*P(D=1)+P(F|D=2)*P(D=2)+P(F|D=3)*P(D=3))=

.9*.1/(.1*.3+.2*.4+.3*.2+.9*.1)=.09/.26 = 9/26

P(D=0|U) = P(U|D=0)*P(0)/(P(U|D=0)*P(D=0)+P(U|D=1)*P(D=1)+P(U|D=2)*P(D=2)+P(U|D=3)*P(D=3))=

.8*.3/(.8*.3+.3*.4+.1*.2+.1*.1)=.24/.39 = 8/13

P(D=1|U) = P(U|D=1)*P(1)/(P(U|D=0)*P(D=0)+P(U|D=1)*P(D=1)+P(U|D=2)*P(D=2)+P(U|D=3)*P(D=3))=

.3*.4/(.8*.3+.3*.4+.1*.2+.1*.1)=.12/.39 = 4/13

P(D=2|U) = P(U|D=`)*P(`)/(P(U|D=0)*P(D=0)+P(U|D=1)*P(D=1)+P(U|D=2)*P(D=2)+P(U|D=3)*P(D=3))=

.1*.2/(.8*.3+.3*.4+.1*.2+.1*.1)=.02/.39 = 2/39

P(D=3|U) = P(U|D=3)*P(3)/(P(U|D=0)*P(D=0)+P(U|D=1)*P(D=1)+P(U|D=2)*P(D=2)+P(U|D=3)*P(D=3))=

.1*.1/(.8*.3+.3*.4+.1*.2+.1*.1)=.01/.39 = 1/39

P(N|D=0 = 1-.1-.8 = .1

P(N|D=1) = 1 - .2 - .3 = .5

P(N|D=2) = 1 - .3 - .1 = .6

P(N|D=3) = 1 - .9 - .1 = 0

P(D=0|N) = P(N|D=0)*P(D=0)/(P(N|D=0)*P(D=0)+P(N|D=1)*P(D=1)+P(N|D=2)*P(D=2)+P(N|D=3)*P(D=3))=.1*.3/(.1*.3+.5*.4+.6*.2+.0*.1)= .03/.35 = 3/35

P(D=1|N) = P(N|D=1)*P(D=0)/(P(N|D=0)*P(D=0)+P(N|D=1)*P(D=1)+P(N|D=2)*P(D=2)+P(N|D=3)*P(D=3))= .5*.4/(.1*.3+.5*.4+.6*.2+.0*.1)= .20/.35 = 4/7

P(D=2|N) = P(N|D=2)*P(D=2)/(P(N|D=0)*P(D=0)+P(N|D=1)*P(D=1)+P(N|D=2)*P(D=2)+P(N|D=3)*P(D=3))= .6*.2/(.1*.3+.5*.4+.6*.2+.0*.1)= .12/.35 = 12/35

P(D=3|N) = 0

If the result of the survey is an F, we have

P(D=0|F) = 3/26

P(D=1|F) = 4/13

P(D=2|F) = 3/13

P(D=3|F) = 9/26

If the order is 0, the return is -25*(1*4/13+2*3/13+3*9/26) = -25*47/26 = -1175/26 = -$45.19

If the order is 1, the return is 3/26*-70+(1-3/26)*80+-25*(1*3/13+2*9/26) = 515/13 = $39.62

If the order is 2, the return is (3/26*2+4/13)*-70+(1*4/13+2*(3/13+9/26))*80 + -25*9/26 =

1835/26 = $70.58

If the order is 3, the return is (3/26*3+4/13*2+3/13)*-70+(1*4/13+2*3/13+3*9/26)*80 =

795/13 = $61.15

We should order 2.

P(D=0|U) = 8/13

P(D=1|U) = 4/13

P(D=2|U) = 2/39

P(D=3|U) = 1/39

If we order 0, the return is (4/13*1+2/39*2+1/39*3)*-25 = -475/39 = -$12.18

If the order is 1, the return is 8/13*-70+(1-8/13)*80+-25*(1*2/39+2*1/39) =-580/39= -14.87

If the order is 2, the return is (8/13*2+4/13)*-70+(1*4/13+2*(2/39+1/39))*80 + -25*1/39 =

-2785/39= -$71.41

If the order is 3, the return is (8/13*3+4/13*2+2/39*1)*-70+(1*4/13+2*2/39+3*1/39)*80 =

-1780/13 = -$136.92

Order 0

P(D=0|N) = 3/35

P(D=1|N) = 4/7

P(D=2|N) = 12/35

P(D=3|N) = 0

If we order 0, the return is (4/7*1+12/35*2)*-25 = -220/7 = -$31.43

If the order is 1, the return is 3/35*-70+(1-3/35)*80+-25*(1*12/35) = 410/7 = $58.57

If the order is 2, the return is (3/35*2+4/7)*-70+(1*4/7+2*12/35)*80 = 340/7 = $48.57

We don't order 3, as the probability of 3 is 0

we order 1

We order 2 if there is an F, 0 if there is an N, and 1 if there is a U.

d) P(F) = .26

P(N) = .39

P(U) = .35

Then, the expected return is .26*1835/26 +-475/39*.39 + 410/7*.35 = $34.10

Since we make $25 if we just take 1, we should pay up to $34.10-$25 = $9.10 for the survey.

hi,

henry is an economist and wants to understand the relationship between inflation and consumer spending habits. for his research, he needs the consumer price index for 2014 and the inflation rate. based on the prices of goods given, what will he find to be the cpi and inflation rate for 2014? assume that a consumer’s basket for three consecutive years consists of the following:

you dont privide answer choices.

answer - 15% of a inflatation rate is 15% less in cpi