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-.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
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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
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............... 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 = - ~ X + 8 ...................................................................... 26
Gambar4.1 Gambar 4.2
Kurva Permintaan .................................................................................................... 30 Kurva Permintaan Persamaan Q = 300 - ~P ...............................................31
Gambar4.3
Persamaan Garis
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
Kurva Permintaan Khusus .................................................................................... 33 Kurva Penawaran (Kurva Positif) ....................................................................... 35 1 Kurva Penawaran Qs = P - 800 ........................................................... 37 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
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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.
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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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