Matematika Ekonomi Bisnis Edisi 2
ｾﾧ＠
,
Elisabet Siahaan
-.DAFTARISI
KATA PENGANTAR..................................................................................................................
DAFT AR lSI ................................................................................................................................
DAFT AR GAMBAR ................................................................ ;.................................................
iii
iv
vi
BAB 1 SIFAT-SIFAT MATEMATIKA EKONOMI DAN BISNIS.....................................
1.1 Matematika Ekonomi dan Matematika Murni.................................................
1.2 Teori Ekonomi, Matematika Ekonomi, Ekonometrika, dan Statistika
Ekonomi .........................................................................................................................
1
1
BAB 2 MODEL EKONOMI......................................................................................................
2.1 Pendahuluan..................................................................................................................
2.2 Variabel, Konstanta, Koefisien, dan Parameter ..............................................
2.3 Persamaan dan Pertidaksamaan...........................................................................
2.4 Sistem Bilangan Nyata ..............................................................................................
2.5 Aturan Pemangkatan dan Pemfaktoran Pemangkatan ...............................
Soal-Soal Latihan...........................................................................................................
3
3
3
4
5
7
14
2
BAB 3 FUNGSI LINIER............................................................................................................ 17
3.1 Pendahuluan.................................................................................................................. 17
3.2 Kemiringan dan Titik Potong Sumbu .................................................................. 17
3.3 Bentuk Umum Fungsi Linier .................................................................................. 18
3.4 Menentukan Persamaan Garis ............................................................................... 22
Soal-Soal Latihan ....................................................................................... :.................. 27
BAB 4 PENERAPAN FUNGSI LINIER ..................................................................................
4.1 Pendahuluan..................................................................................................................
4.2 Fungsi Permintaan......................................................................................................
4.3 Fungsi Penawaran.......................................................................................................
4.4 Keseimbangan Pasar Satu Macam Produk.......... ..............................................
4.5 Keseimbangan Pasar Dua Macam Produk.........................................................
4.6 Pengaruh Pajak Pada Kesimbangan Pasar ........................................................
4.7 Pengaruh Subsidi Pad a Keseimbangan Pasar............ ......................................
4.8 Analisis Pulang Pokok................................................................................................
4.9 Fungsi Konsumsi dan Tabungan ...........................................................................
4.10 Model Penentuan Pendapatan Nasional............................................................
Soal-Soal Latihan.........................................................................................................
28
28
28
34
38
42
45
51
55
59
62
65
BAB 5 FUNGSI NON LINIER DAN PENERAPANNYA DALAM EKONOMI
DAN BISNIS .................................................................................................................. 70
5.1 Pendahuluan.................................................................................................................. 70
5.2 Fungsi Permintaan...................................................................................................... 70
5.3 Fungsi Penawaran ....................................................................................................... 79
5.4 Keseimbangan Pasar .................................................................................................. 82
IV
5.5
__ ,, 0:: •...,•••••••••••••••••••
iii
iv
vi
1
1
2
3
3
3
4
5
7
14
17
17
17
18
.... ............. 22
27
28
. . . ... .............
28
28
34
38
42
45
51
55
59
62
65
Fungsi Penerimaan Total.......................................................................................... 87
Soal-Soal Latihan.......................................................................................................... 90
BAB 6 BARIS DAN DERET SERTA PENERAPANNYA DALAM EKONOMI
DAN BISNIS ................................................................................................................. 92
6.1 Pendahuluan..................................................................................................................
6.2 Bunga Sederhana dan Potongan Sederhana ...................................................
6.3 Bunga Majemuk............................................................................................................
6.4 Anuitas .............................................................................................................................
6.5 Dana Cadangan Atau Dana Pelunasan (Sinking Fund) ................................
6.6 Penyisihan Pinjaman (Loan Amortization) ...................................................
Soal-Soal Latihan ..........................................................................................................
92
92
94
97
100
101
105
BAB 7 KALKULUS DIFERENSIAL DAN PENERAPANNYA DALAM EKONOMI
DAN BISNIS: FUNGSI DENGAN SATU VARIABEL BEBAS ............................... 108
7.1 Pendahuluan ..................................................................................................................
7.2 Elastisitas Permintaan dan Penawaran ..............................................................
7.3 Penerapan Optimisasi: Fungsi dengan Satu Variabel Bebas ......................
7.4 Biaya Total (TC), Biaya Rata-Rata (AC), dan Biaya Marginal (MC) ........
7.5 Penerimaan Total, Rata-Rata, dan MarginaL ...................................................
7.6 Laba Maksimum .........................................................................................................
Soal-Soal Latihan ............................................................................... :.........................
108
108
116
117
120
124
125
BAB 8 PENERAPAN KALKULUS DIFERENSIAL DALAM EKONOMI DAN BISNIS:
FUNGSI DENGAN DUA VARIABEL BEBAS ....................................................... 128
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Pendahuluan ..................................................................................................................
Biaya Marginal ..............................................................................................................
Elastisitas Permintaan Parsial ...............................................................................
Fungsi Produksi ............................................................................................................
Penerapan Optimisasi: Fungsi dengan Dua Variabel Bebas ......................
Laba Maksimum dengan Dua Input .....................................................................
Penerapan Optimisasi Terkendala dalam Ekonomi dan Bisnis ................
Soal-Soal Latihan ..........................................................................................................
128
128
129
132
133
138
139
142
DAFTAR BACAAN .................................................................................................................... 146
(J'll
_
............... 70
.... ., ...........
70
... .............. 70
... .............. 79
..... .. ........... 82
v
DAFTAR GAMBAR
Gambar 2.1.
Gambar 3.1
Gambar 3.2
Gambar 3.3
Gambar 3.4
Gambar 3.5
Gambar 3.6
Sistem Bilangan Nyata ............................................................................................. 6
Empat Jenis Kemiringan pada Garis Linier ....................................................... 19
Persamaan garis implisit. 15X +3Y -24 = 0 ................................................... 21
Kemiringan Garis ....................................................................................................... 22
Persamaan garis Y = 16- 2X .................................................................................. 23
Persamaan garis Y = -4+3X ................................................................................. 24
Persamaan garis Y = - ｾ＠ X + 8 ...................................................................... 26
Gambar4.1
Gambar 4.2
Kurva Permintaan .................................................................................................... 30
...............................................31
Kurva Permintaan Persamaan Q = 300 - ｾｐ＠
Gambar4.3
Gambar4.4
Gambar 4.5
Gambar 4.6
Gambar 4.7
Gambar 4.8
Gambar4.9
Gambar 4.10
Gambar 4.11
Gambar4.12
Gambar4.13
Gambar4.14
Gambar 4.15
Gambar 4.16
Gambar 4.17
Gambar 4.18
Gambar4.19
Gambar4.20
Gambar 4.21
Gambar 5.1
Gambar 5.2
Gambar 5.3
Gambar 5.4
Gambar 5.5
Gambar 5.6
Gambar 5.7
Gambar 5.8
Gambar 5.9
1
Q = 1.100 - - p ................................................................. 32
10
Kurva Permintaan Qd =q+21-3p .......................................................................... 33
Persamaan Garis
Kurva Permintaan Khusus .................................................................................... 33
Kurva Penawaran (Kurva Positif) ....................................................................... 35
1
P - 800 ........................................................... 37
Kurva Penawaran Qs =
20.000
Kurva Penawaran Khusus ........................................................................................ 38
Keseimbangan Pasar ................................................................................................ 38
Keseimbangan Pasar yang Tidak Mempunyai Arti Ekonomi.. .................... 39
Keseimbangan Pasar .................................................................................................. 40
Grafik Keseimbangan Pasar ................................................................................... 41
Keseimbangan Pasar Mula-Mula dan Setelah Kena Pajak ......................... 46
Grafik Keseimbangan Pasar Mula-Mula Setelah Kena Pajak .................... ..49
Grafik Keseimbangan Pasar Setelah Kena Pajak .............................................. 50
Grafik Subsidi yang Dinikmati Konsumen ......................................................... 52
Grafik Keseimbangan Pasar Setelah Subsidi ................................................... 53
Grafik Keseimbangan Pasar Setelah Subsidi ..................................................... 55
Titik Pulang pokok (Titik Impas) .......................................................................... 57
Fungsi Konsumsi dan Tabungan ......................................................................... 60
Contoh Grafik Fungsi Konsumsi dan Fungsi Tabungan ............................. 61
Kurva Permintaan dari Parabola yang Terbuka ke Bawah
P =c + bQ - aQ2 dan a < 0 ........................................................................................ 65
Kurva Permintaan Parabola Terbuka ke Kiri Qd = -aP2+bP +c ........... 71
Fungsi Permintaan P = 48 - 3Q2 ............................................................................. 72
Kurva Permintaan dengan Fungsi Q = 21 - 4P - p2 ........................................ 74
Kurva Permintaan Berbentuk Hiperbola ............................................................ 76
Kurva Permintaan ......................................................................................................... 77
Kurva Permintaan PQ = 36 ....................................................................................... 78
Kurva Permintaan dengan Fungsi (Q + 4) ( P + 2) =20 ............................... 79
Kurva Penawaran P = c + bQ + aQ2................................................... 80
Gambar 5.10 Kurva Penawaran dengan Fungsi Q = aP2 + bP + c ......................................... 80
VI
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........... ,................ 6
............................ 19
.......................... 21
............................ 22
..... ...................... 23
........................ 24
.... .................... 26
." ....................... 30
......................... 31
Gambar 5.11 Kurva Fungsi Penawaran Ps =2Q2 + 3Q + 12 ...................................................81
Gambar 5.12 Kurva Fungsi Permintaan Qd =5P2 - lOP ....................................................... 82
Gambar 5.13 Delapan Gambar Keseimbangan Pasar, Kombinasi
Perpotongan Fungsi Permintaan dan Penawaran ....................................... 83
Gambar 5.14 Keseimbangan Pasar .................................................................................................. 84
Gambar 5.15 Keseimbangan Pasar ................................................................................................. 85
Gambar 5.16 Keseimbangan Pasar .................................................................................................. 86
Gambar 5.17 Parabola Terbuka ke Bawah .................................................................................. 87
Gambar 5.18 Kurva Penerimaan Total ......................................................................................... 89
Gambar 7.1 Jenis·Jenis Kurva Elastisitas Permintaan ...................................................... 111
Gambar 7.2 Jenis-Jenis Kurva Elastisitas Penawaran .................................................... 114
......................... 32
_ _ ...................... 33
__ ... .. .............. 33
ｾ＠
,. ___ .................... 35
ｾ｟＠
.................. 37
_ _ ................. 38
_ _ _ ............. ... 38
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........... .. 39
r.--_ _ｾ＠ .......... 40
F.--_ _ _ ,,_ .. .. ... 41
_ _ _......... 46
.= ］Ｎｾ＠ __ ......... 49
_ _ _ ......... 50
ｾ＠
_ _ _ ........ 52
r _ _ _ _ ........ 53
r.--_ _ _ ......... 55
ｾ＠ _ _ _ｾ＠
......... 57
r ____· .. ·.. ·.. ·60
I
............ 61
ｾ＠
____ｾ
Ｎｵ＠
........ 65
.. ......... 71
_ _ _ ..... ........ 72
ｾ＠
___ .. ........... 74
r-- - - ............. 76
ｾ＠
____ ............ 77
ｾ＠ _ _ _.............. 78
_ _ _ .............. 79
....... ... ..... 80
_ _ _ ... ........... 80
vii
DAFTAR BACAAN
Chiang C. Alpha dan Wainwrigh Kevin. 2006. Dasar-Dasar Matematika Ekonomi,
Penerbit Erlangga, Jakarta
Dowling T. Edward. 1992. Matematika untuk Ekonomi, Cetakan Kedua, Penerbit
Erlangga, Jakarta
Dumairy. 2003. Matematika Terapan untuk Bisnis dan Ekonomi, Cetakan Pertama,
BPFE-Yogyakarta.
Kalangi Bintang Josep. 2006. Matematika Ekonomi dan Bisnis, Edisi Pertama, Jilid
Pertama dan Kedua, Penerbit Salemba Empat, Jakarta.
Salvatore, Dominick. 2005. Ekonomi Manajerial dalam Perekonomian Global, Edisi
Kelima, Buku I, Salemba Empat, Jakarta.
Siahaan Elisabet. 2012. Ekonomi Manajerial, Edisi Pertama, USU Press, Medan.
Simamora Tuana. 2004. Matematika Ekonomi, Fakultas Ekonomi Universitas Sumatera
Utara, Medan
Weber, E. Jean. 1982. Mathematical Analysis: Business and Economics Application,
Fourth Edition, Edition, New York: Harper & Row, Publisher, Inc.
146
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Dr. Elisabet Siahaan, SE., M.Ec. adalah dosen Departemen
Manajemen pada Fakultas Ekonomi Universitas Sumatera
Utara (USU). Lahir di Medan, pada tanggal13 Maret 1978. Gelar
Sarjana Ekonomi (SE) diperoleh dari FE USU tahun 2000 awal.
Tahun 2000 pertengahan melanjutkan kuliah pada program
studi Pascasarjana pada Fakultas Ekonomi di Universitas
Malaya (UM), Kuala Lumpur, Malaysia. Tahun 2002 awal
mendapat gelar Master of Economics. Setelah tamat dari Kuala
Lumpur kembali ke Indonesia bekerja sebagai dosen di
beberapa universitas swasta, dan Desember 2002 diangkat
menjadi staf pengajar tetap FE-USU sampai sekarang. Tahun
2004 melanjutkan pendidikan Strata 3 (S3) di Universitas
Brawijaya (UNIBRAW) Malang-Jatim dan menyelesaikan
pendidikan S3 pada tahun 2007 dengan kekhususan
Manajemen Sumber Daya Manusia.
•
,
Elisabet Siahaan
-.DAFTARISI
KATA PENGANTAR..................................................................................................................
DAFT AR lSI ................................................................................................................................
DAFT AR GAMBAR ................................................................ ;.................................................
iii
iv
vi
BAB 1 SIFAT-SIFAT MATEMATIKA EKONOMI DAN BISNIS.....................................
1.1 Matematika Ekonomi dan Matematika Murni.................................................
1.2 Teori Ekonomi, Matematika Ekonomi, Ekonometrika, dan Statistika
Ekonomi .........................................................................................................................
1
1
BAB 2 MODEL EKONOMI......................................................................................................
2.1 Pendahuluan..................................................................................................................
2.2 Variabel, Konstanta, Koefisien, dan Parameter ..............................................
2.3 Persamaan dan Pertidaksamaan...........................................................................
2.4 Sistem Bilangan Nyata ..............................................................................................
2.5 Aturan Pemangkatan dan Pemfaktoran Pemangkatan ...............................
Soal-Soal Latihan...........................................................................................................
3
3
3
4
5
7
14
2
BAB 3 FUNGSI LINIER............................................................................................................ 17
3.1 Pendahuluan.................................................................................................................. 17
3.2 Kemiringan dan Titik Potong Sumbu .................................................................. 17
3.3 Bentuk Umum Fungsi Linier .................................................................................. 18
3.4 Menentukan Persamaan Garis ............................................................................... 22
Soal-Soal Latihan ....................................................................................... :.................. 27
BAB 4 PENERAPAN FUNGSI LINIER ..................................................................................
4.1 Pendahuluan..................................................................................................................
4.2 Fungsi Permintaan......................................................................................................
4.3 Fungsi Penawaran.......................................................................................................
4.4 Keseimbangan Pasar Satu Macam Produk.......... ..............................................
4.5 Keseimbangan Pasar Dua Macam Produk.........................................................
4.6 Pengaruh Pajak Pada Kesimbangan Pasar ........................................................
4.7 Pengaruh Subsidi Pad a Keseimbangan Pasar............ ......................................
4.8 Analisis Pulang Pokok................................................................................................
4.9 Fungsi Konsumsi dan Tabungan ...........................................................................
4.10 Model Penentuan Pendapatan Nasional............................................................
Soal-Soal Latihan.........................................................................................................
28
28
28
34
38
42
45
51
55
59
62
65
BAB 5 FUNGSI NON LINIER DAN PENERAPANNYA DALAM EKONOMI
DAN BISNIS .................................................................................................................. 70
5.1 Pendahuluan.................................................................................................................. 70
5.2 Fungsi Permintaan...................................................................................................... 70
5.3 Fungsi Penawaran ....................................................................................................... 79
5.4 Keseimbangan Pasar .................................................................................................. 82
IV
5.5
__ ,, 0:: •...,•••••••••••••••••••
iii
iv
vi
1
1
2
3
3
3
4
5
7
14
17
17
17
18
.... ............. 22
27
28
. . . ... .............
28
28
34
38
42
45
51
55
59
62
65
Fungsi Penerimaan Total.......................................................................................... 87
Soal-Soal Latihan.......................................................................................................... 90
BAB 6 BARIS DAN DERET SERTA PENERAPANNYA DALAM EKONOMI
DAN BISNIS ................................................................................................................. 92
6.1 Pendahuluan..................................................................................................................
6.2 Bunga Sederhana dan Potongan Sederhana ...................................................
6.3 Bunga Majemuk............................................................................................................
6.4 Anuitas .............................................................................................................................
6.5 Dana Cadangan Atau Dana Pelunasan (Sinking Fund) ................................
6.6 Penyisihan Pinjaman (Loan Amortization) ...................................................
Soal-Soal Latihan ..........................................................................................................
92
92
94
97
100
101
105
BAB 7 KALKULUS DIFERENSIAL DAN PENERAPANNYA DALAM EKONOMI
DAN BISNIS: FUNGSI DENGAN SATU VARIABEL BEBAS ............................... 108
7.1 Pendahuluan ..................................................................................................................
7.2 Elastisitas Permintaan dan Penawaran ..............................................................
7.3 Penerapan Optimisasi: Fungsi dengan Satu Variabel Bebas ......................
7.4 Biaya Total (TC), Biaya Rata-Rata (AC), dan Biaya Marginal (MC) ........
7.5 Penerimaan Total, Rata-Rata, dan MarginaL ...................................................
7.6 Laba Maksimum .........................................................................................................
Soal-Soal Latihan ............................................................................... :.........................
108
108
116
117
120
124
125
BAB 8 PENERAPAN KALKULUS DIFERENSIAL DALAM EKONOMI DAN BISNIS:
FUNGSI DENGAN DUA VARIABEL BEBAS ....................................................... 128
8.1
8.2
8.3
8.4
8.5
8.6
8.7
Pendahuluan ..................................................................................................................
Biaya Marginal ..............................................................................................................
Elastisitas Permintaan Parsial ...............................................................................
Fungsi Produksi ............................................................................................................
Penerapan Optimisasi: Fungsi dengan Dua Variabel Bebas ......................
Laba Maksimum dengan Dua Input .....................................................................
Penerapan Optimisasi Terkendala dalam Ekonomi dan Bisnis ................
Soal-Soal Latihan ..........................................................................................................
128
128
129
132
133
138
139
142
DAFTAR BACAAN .................................................................................................................... 146
(J'll
_
............... 70
.... ., ...........
70
... .............. 70
... .............. 79
..... .. ........... 82
v
DAFTAR GAMBAR
Gambar 2.1.
Gambar 3.1
Gambar 3.2
Gambar 3.3
Gambar 3.4
Gambar 3.5
Gambar 3.6
Sistem Bilangan Nyata ............................................................................................. 6
Empat Jenis Kemiringan pada Garis Linier ....................................................... 19
Persamaan garis implisit. 15X +3Y -24 = 0 ................................................... 21
Kemiringan Garis ....................................................................................................... 22
Persamaan garis Y = 16- 2X .................................................................................. 23
Persamaan garis Y = -4+3X ................................................................................. 24
Persamaan garis Y = - ｾ＠ X + 8 ...................................................................... 26
Gambar4.1
Gambar 4.2
Kurva Permintaan .................................................................................................... 30
...............................................31
Kurva Permintaan Persamaan Q = 300 - ｾｐ＠
Gambar4.3
Gambar4.4
Gambar 4.5
Gambar 4.6
Gambar 4.7
Gambar 4.8
Gambar4.9
Gambar 4.10
Gambar 4.11
Gambar4.12
Gambar4.13
Gambar4.14
Gambar 4.15
Gambar 4.16
Gambar 4.17
Gambar 4.18
Gambar4.19
Gambar4.20
Gambar 4.21
Gambar 5.1
Gambar 5.2
Gambar 5.3
Gambar 5.4
Gambar 5.5
Gambar 5.6
Gambar 5.7
Gambar 5.8
Gambar 5.9
1
Q = 1.100 - - p ................................................................. 32
10
Kurva Permintaan Qd =q+21-3p .......................................................................... 33
Persamaan Garis
Kurva Permintaan Khusus .................................................................................... 33
Kurva Penawaran (Kurva Positif) ....................................................................... 35
1
P - 800 ........................................................... 37
Kurva Penawaran Qs =
20.000
Kurva Penawaran Khusus ........................................................................................ 38
Keseimbangan Pasar ................................................................................................ 38
Keseimbangan Pasar yang Tidak Mempunyai Arti Ekonomi.. .................... 39
Keseimbangan Pasar .................................................................................................. 40
Grafik Keseimbangan Pasar ................................................................................... 41
Keseimbangan Pasar Mula-Mula dan Setelah Kena Pajak ......................... 46
Grafik Keseimbangan Pasar Mula-Mula Setelah Kena Pajak .................... ..49
Grafik Keseimbangan Pasar Setelah Kena Pajak .............................................. 50
Grafik Subsidi yang Dinikmati Konsumen ......................................................... 52
Grafik Keseimbangan Pasar Setelah Subsidi ................................................... 53
Grafik Keseimbangan Pasar Setelah Subsidi ..................................................... 55
Titik Pulang pokok (Titik Impas) .......................................................................... 57
Fungsi Konsumsi dan Tabungan ......................................................................... 60
Contoh Grafik Fungsi Konsumsi dan Fungsi Tabungan ............................. 61
Kurva Permintaan dari Parabola yang Terbuka ke Bawah
P =c + bQ - aQ2 dan a < 0 ........................................................................................ 65
Kurva Permintaan Parabola Terbuka ke Kiri Qd = -aP2+bP +c ........... 71
Fungsi Permintaan P = 48 - 3Q2 ............................................................................. 72
Kurva Permintaan dengan Fungsi Q = 21 - 4P - p2 ........................................ 74
Kurva Permintaan Berbentuk Hiperbola ............................................................ 76
Kurva Permintaan ......................................................................................................... 77
Kurva Permintaan PQ = 36 ....................................................................................... 78
Kurva Permintaan dengan Fungsi (Q + 4) ( P + 2) =20 ............................... 79
Kurva Penawaran P = c + bQ + aQ2................................................... 80
Gambar 5.10 Kurva Penawaran dengan Fungsi Q = aP2 + bP + c ......................................... 80
VI
ｾ＠
........... ,................ 6
............................ 19
.......................... 21
............................ 22
..... ...................... 23
........................ 24
.... .................... 26
." ....................... 30
......................... 31
Gambar 5.11 Kurva Fungsi Penawaran Ps =2Q2 + 3Q + 12 ...................................................81
Gambar 5.12 Kurva Fungsi Permintaan Qd =5P2 - lOP ....................................................... 82
Gambar 5.13 Delapan Gambar Keseimbangan Pasar, Kombinasi
Perpotongan Fungsi Permintaan dan Penawaran ....................................... 83
Gambar 5.14 Keseimbangan Pasar .................................................................................................. 84
Gambar 5.15 Keseimbangan Pasar ................................................................................................. 85
Gambar 5.16 Keseimbangan Pasar .................................................................................................. 86
Gambar 5.17 Parabola Terbuka ke Bawah .................................................................................. 87
Gambar 5.18 Kurva Penerimaan Total ......................................................................................... 89
Gambar 7.1 Jenis·Jenis Kurva Elastisitas Permintaan ...................................................... 111
Gambar 7.2 Jenis-Jenis Kurva Elastisitas Penawaran .................................................... 114
......................... 32
_ _ ...................... 33
__ ... .. .............. 33
ｾ＠
,. ___ .................... 35
ｾ｟＠
.................. 37
_ _ ................. 38
_ _ _ ............. ... 38
Ｎｵ｟ｾ＠
........... .. 39
r.--_ _ｾ＠ .......... 40
F.--_ _ _ ,,_ .. .. ... 41
_ _ _......... 46
.= ］Ｎｾ＠ __ ......... 49
_ _ _ ......... 50
ｾ＠
_ _ _ ........ 52
r _ _ _ _ ........ 53
r.--_ _ _ ......... 55
ｾ＠ _ _ _ｾ＠
......... 57
r ____· .. ·.. ·.. ·60
I
............ 61
ｾ＠
____ｾ
Ｎｵ＠
........ 65
.. ......... 71
_ _ _ ..... ........ 72
ｾ＠
___ .. ........... 74
r-- - - ............. 76
ｾ＠
____ ............ 77
ｾ＠ _ _ _.............. 78
_ _ _ .............. 79
....... ... ..... 80
_ _ _ ... ........... 80
vii
DAFTAR BACAAN
Chiang C. Alpha dan Wainwrigh Kevin. 2006. Dasar-Dasar Matematika Ekonomi,
Penerbit Erlangga, Jakarta
Dowling T. Edward. 1992. Matematika untuk Ekonomi, Cetakan Kedua, Penerbit
Erlangga, Jakarta
Dumairy. 2003. Matematika Terapan untuk Bisnis dan Ekonomi, Cetakan Pertama,
BPFE-Yogyakarta.
Kalangi Bintang Josep. 2006. Matematika Ekonomi dan Bisnis, Edisi Pertama, Jilid
Pertama dan Kedua, Penerbit Salemba Empat, Jakarta.
Salvatore, Dominick. 2005. Ekonomi Manajerial dalam Perekonomian Global, Edisi
Kelima, Buku I, Salemba Empat, Jakarta.
Siahaan Elisabet. 2012. Ekonomi Manajerial, Edisi Pertama, USU Press, Medan.
Simamora Tuana. 2004. Matematika Ekonomi, Fakultas Ekonomi Universitas Sumatera
Utara, Medan
Weber, E. Jean. 1982. Mathematical Analysis: Business and Economics Application,
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Dr. Elisabet Siahaan, SE., M.Ec. adalah dosen Departemen
Manajemen pada Fakultas Ekonomi Universitas Sumatera
Utara (USU). Lahir di Medan, pada tanggal13 Maret 1978. Gelar
Sarjana Ekonomi (SE) diperoleh dari FE USU tahun 2000 awal.
Tahun 2000 pertengahan melanjutkan kuliah pada program
studi Pascasarjana pada Fakultas Ekonomi di Universitas
Malaya (UM), Kuala Lumpur, Malaysia. Tahun 2002 awal
mendapat gelar Master of Economics. Setelah tamat dari Kuala
Lumpur kembali ke Indonesia bekerja sebagai dosen di
beberapa universitas swasta, dan Desember 2002 diangkat
menjadi staf pengajar tetap FE-USU sampai sekarang. Tahun
2004 melanjutkan pendidikan Strata 3 (S3) di Universitas
Brawijaya (UNIBRAW) Malang-Jatim dan menyelesaikan
pendidikan S3 pada tahun 2007 dengan kekhususan
Manajemen Sumber Daya Manusia.
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