Section 13.1 Problem 4. The reward matrix is computed to be: Noble

March 10, 2018 | Author: Anonymous | Category: History, European History, Renaissance (1330-1550), Feudalism

Short Description

Download Section 13.1 Problem 4. The reward matrix is computed to be: Noble...

Description

Section 13.1 Problem 4. The reward matrix is computed to be: Noble Greek Price Pizza King Price \$6 \$8 \$10 ---------------------------------------------\$5 \$125 \$175 \$225 ---------------------------------------------\$6 \$200 \$300 \$400 ---------------------------------------------\$7 \$225 \$375 \$525 ---------------------------------------------\$8 \$200 \$400 \$600 ---------------------------------------------\$9 \$125 \$375 \$625 ----------------------------------------------

Pizza King Charges Minimum Reward * ---------------------------------------------\$5 \$125 ---------------------------------------------\$6 \$200 ---------------------------------------------\$7 \$225* ---------------------------------------------\$8 \$200 ---------------------------------------------\$9 \$125 ---------------------------------------------Thus, maximin action is to charge \$7. To determine maximax action look at: Pizza King Charges Maximum Reward ---------------------------------------------\$5 \$225 ---------------------------------------------\$6 \$400 ---------------------------------------------\$7 \$525 ---------------------------------------------\$8 \$600 ---------------------------------------------\$9 \$625* ---------------------------------------------Thus, maximax action is to charge \$9.

The regret matrix is Pizza King Price Noble Greek Price ---------------------------------------------\$6 \$8 \$10 Maximum Regret ---------------------------------------------\$5 \$100 \$225 \$400 \$400 ---------------------------------------------\$6 \$25 \$100 \$225 \$225 ---------------------------------------------\$7 \$0 \$25 \$100 \$100 ---------------------------------------------\$8 \$25 \$0 \$25 \$25* ---------------------------------------------\$9 \$100 \$25 \$0 \$100 ---------------------------------------------Thus, minimax regret action is to charge \$8. Expected reward for for for for for

\$5 \$6 \$7 \$8 \$9

= = = = =

\$175 \$300 \$375 \$400 \$375

Thus, Pizza King maximizes their expected reward by charging \$8. Section 13.2 Problem 3. Since u''(x) = 0, I am now risk neutral. E(U for L1) = 2(19,000) + 1 = 38,001 E(U for L2) = 0.1(20,001) + 0.9(40,001) = 38,001 Thus, I am indifferent between L1 and L2. (This is because a risk neutral decision maker chooses between lotteries on basis of expected value and L1 and L2 have same expected value. Let x = CE(L2). Then 2x + 1 = 38,001 or x = \$19,000. Thus RP for L2 = 19,000 - 19,000 = \$0. Problem 7. Let u(A) = 1 and u(D) = 0. Then u(C) = .25,u(B) = .70 and OR course has expected utility of 0.10(1) + 0.4(0.70) + 0.5(0.25) = 0.505 Statistics course has expected utility of 0.7(0.70) + 0.25(0.25) + 0.1(0) = 0.5525. Thus, Statistics course should be taken. Problem 10. Hiring CPA has expected utility of 0.2u(35,500) + 0.8u(31,500) = 0.2(35,500)1/2 + 0.8(31,500)1/2 = 179.7

while Not Hiring CPA has expected utility of (32,000)1/2 = 178.9. Thus, the CPA should be hired. Problem 16. (a) Let b = buying price of lottery. Then I am indifferent between 1/2 10,000 + 1,025 - b ----1/2 10,000 – 199 - b ----and 1 10,000 -----Then 100 = 1/2(11,025 - b)1/2 + 1/2(9801 - b)1/2. (b) Let s = minimum selling price. Then I am indifferent between

1/2 11,025 -----1/2 9,801 and ------1 10,000 + s or -------(10,000 + s)1/2 = 1/2(11,025)1/2 + 1/2(9,801)1/2 = 1/2(105 + 99) = 102 or 10,000 + s = 10,404 and s = \$404 (c) Now we are indifferent between 1/2 2,025 ---1/2 801 ____ and 1 1,000 + s ----Thus, (1,000 + s)1/2 = 1/2(2025)1/2 + 1/2(801)1/2 = 1/2{45 + 28.30} Therefore, 1000 + s = 1,343.22 and s = \$343.22. Thus, the selling price of the lottery (and indeed, the buying price for the lottery) depends on our current asset position.

(d) Let a = asset position, b = buying price of lottery and s = selling price of lottery. Then I am indifferent between 1/2 -----

a - b + 1,025

1/2 a - b - 199 -----and 1 a . -----I am also indifferent between 1/2 a + 1,025 ------1/2 a - 199 -------

and

1 a + s ------Thus we have that 1/2(1 - eb-a-1025) + 1/2(1-eb-a + 199) = 1 – e-a or -1/2(eb-a[e-1025 + e199] = -e-a. Thus, eb = 2/(e-1025 + e199) and for all asset positions b = ln {2/(e-1025 + e199)) We also know that 1/2(1 – e-a-1025) + 1/2(1 - e199-a) = 1 – e-a-s. Thus, -e-a(e-1025 + e199)/2 = -e-a-s or e-s = (e-1025 + e199)/2 and s = ln {2/(e-1025 + e199)}. Thus, both the buying and selling price for the lottery are independent of current asset position and are equal! Section 13.4 Problem 1. Hire geologist. If favorable report, we drill; if unfavorable report, do not drill. Expected net profits = \$180,000. EVWSI = \$190,000 EVWOI = \$170,000. EVSI = \$190,000 - \$170,000 = \$20,000. Since EVSI is greater than the cost of geologist, we should hire geologist.

Section 13.5 Problem 3. P(cold forecast) =0.9(0.4) + 0.2(0.6) = 0.48, P(warm forcast) = 1 -0.48 = 0.52. P(cold P(warm P(cold P(warm

year|cold year|cold year|warm year|warm

forecast) = 0.36/0.48 = 0.75, forcast) = 0.12/0.48 = 0.25, forecast) = (0.1)(0.4)/0.52 = 1/13, forecast) = (0.8)(0.6)/0.52 = 12/13.

Thus, test should not be taken and either wheat or corn can be planted. EVWSI = 6620 + 600 = 7220 EVSI =7220 – 6800 = 420

EVWPI = 7400, EVWOI = 6800, and EVPI = 7400 – 6800 = 600.