Latihan soal decision making
• Ann Tyler baru mendapat warisan peninggalan dari kakek dan neneknya. Ia sedang mencoba memutuskan satu dari beberapa alternatif investasi. Tingkat pengembalian setelah 1 tahun sangat bergantung pada tingkat bunga selama tahun berikutnya. Saat ini tingkat bunga adalah 7% dan ia mengantisipasi bahwa tingkat bunga tersebut akan tetap sama atau meningkat atau menurun sebesar-besarnya 2 point. Berbagai alternatif investasi beserta tingkat pengembaliannya ($10,000an) berdasarkan tingkat bunga tertentu ditunjukkan dalam tabel berikut ini. Tentukan investasi yang terbaik dengan menggunakan kriteria keputusan berikut ini. (Persoalan decision making)
investasi Dana pasar uang Dana pertumbuhan modal
5% 2 -3
Tingkat bunga 6% 7% 8% 3.1 4 4.3 -2 2.5 4
9% 5 6
Dana obligasi Dana pemerintah Dana resiko Tabungan obligasi
6 4 -9 3
5 3.6 -4.5 3
2 2.8 14.7 3.5
3 3.2 1.2 3.2
3 3 8.3 3.4
• Maximax • Berdasarkan kriteria keputusan maximax payoff, maka Ann Tyler akan menginvestasikan warisannya di dana risiko dengan tingkat pengembalian sebesar $147.000 • Maximin • Berdasarkan kriteria keputusan maximin payoff, maka Ann Tyler akan menginvestasikan warisannya di Tabungan obligasi dengan tingkat pengembalian sebesar $30.000
• Equally likely = insufficien reason Berdasarkan kriteria keputusan equally like maka terdapat alternatif investasi yaitu sebagai berikut : • Dana pasar uang = 3.68 * 10.000 = 36.800 • Dana pertumbuhan modal = 1.5 * 10.000 = 15000 • Dana obligasi = 38.000 • Dana pemerintah= 33.200 • Dana risiko = 21.400 • Tabungan olbigasi = 32.200 • Jadi sesuai kriteria keputsan equally likely maka dipilih yang terbesar yaitu dana obligasi dengan tingkat pengembalian sebesar $38.000 • • Minimax • Jika Ann Tyler berkarakteristik pesimistik dan meminimalisasi penyesalan maka Ann akan memilih kriteria keputusan minimax regret dan menginvestasikan di dana pertumbuhan modal dengan tingkat pengembalian sebesar $90.000
Maximin Criterion 5% 2
dana pasar uang dana pertumbuhan modal dana obligasi dana pemerintah dana resiko tabungan obligasi
maximin payoff maximin decision
maximax payoff maximax decision
10.000 6% 3.1
7% 4
8% 4.3
9% 5
9.2
minimum maximal 2 5
-3 6
-2 5
2.5 3
4 3
6 2
3.75 9.5
-3 2
6 6
4 -9 3
3.6 -4.5 3
3.2 1.2 3.2
3 8.3 3.4
2.8 14.7 3.5
8.3 5.35 8.05
2.8 -9 3
4 14.7 3.5
3
30.000
3.8
38.000
tabungan obligasi
14.7
equaly like equaly like decision
dana obligasi
147.000
dana resiko
minimax Regret criterion tabel regret dana pasar uang dana pertumbuhan modal dana obligasi dana pemerintah dana resiko tabungan obligasi
equaly like (laplace)
3.68 1.5 3.8 3.32 2.14 3.22
5% 4
6% 1.9
7% 0
8% 4
9% 9.7
maximum 9.7
9 0 2 15 3
7 0 1.4 9.5 2
1.5 1 0.8 2.8 0.8
4.3 5.3 5.3 0 4.9
8.7 12.7 11.9 0 11.2
9 12.7 11.9 15 11.2
minimax regret payoff 9 90.000 minimax regret decision dana pertumbuhan modal
1.84
• The Campus Bookstore at East Tennessee State University must decide how many economics textbooks to order for the next semester’s class. The bookstore believes that either seven eight, nine, or ten sections of the course will be offered next semester; each section contains 40 students. The publisher is offering bookstores a discount if they place their orders early. If the bookstore orders too few texts and runs out, the publisher will air express additional books at the bookstore’s expense. If it orders too many texts, the store can return unsold texts to the publisher for a partial credit.
• The bookstore is considering ordering either 280, 320, 360, or 400 texts in order to get the discount. Taking into account the discounts, air express expenses, and credits for returned texts, the bookstore manager estimates the following resulting profits. Number of textbooks to order
Number of introductory Economics 7
8
9
10
280
$2800
$2720
$2640
$2480
320
$2600
$3200
$3040
$2880
360
$2400
$3000
$3600
$3440
400
$2200
$2800
$3400
$4000
• What is the optimal decision if the bookstore manager uses the maximax criterion? • What is the optimal decision if the bookstore manager uses the maximin criterion? • What is the optimal decision if the bookstore manager uses the minimax regret criterion?
Number of Introductory Economics classes Tabel Payoff offered
280 text 320 text 360 text 400 text
maximin payoff
7%
8%
9%
10%
minimum
2800 2600 2400 2200
2720 3200 3000 2800
2640 3040 3600 3400
2480 2880 3440 4000
2480 2600 2400 2200
2600
• National Foods has developed a new sports beverage it would like to advertise on Super Bowl Sunday. National’s advertising agency can purchase either one, two, or three 30-second commercials advertising the drink. It estimates that the return will be based on Super Bowl viewership, which in turn, is based on fans’ perception of whether the game is “dull”, “average”, “above average”, or “exciting”. National Foods’ ad agency has constructed the following payoff table giving its estimate of the expected profit (in $100,000’s) resulting from purchasing one, two, or three advertising spots.
• (Another possible decision is for National Foods not to advertise at all during the Super Bowl). The states of nature correspond to the game being “dull”, “average”, “above average”, or “exciting” Number of 30-second commercials purchased
Perceived Game Excitement Dull
Average
Above Average
Exciting
One
-2
3
7
13
Two
-5
6
12
18
Three
-9
5
13
22
• What is the optimal decision if the National Foods advertising manager is optimistic? • What is the optimal decision if the National Foods advertising manager is pessimistic? • What is the optimal decision if the National Foods advertising manager wishes to minimize the firm’s maximum regret?
