# Economic models Consept of sets. Ingredients of mathematical models An economic model is merely a theoretical framework, and there is no inherent reason.

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Economic models Consept of sets

Ingredients of mathematical models An economic model is merely a theoretical framework, and there is no inherent reason why it must be mathematical. Variable is something whose magnitude can change, i.e., something that can take on diferent values. Variables frequantly used in economics include price, profit, revenue, cost, investment. Varieble can assume various values by symbol, we may represent price by P, profit by ∏ revenue by R, cost by C, national income by Y. Constant (α) is a magnitude thas does not change and is therefore antithesis of variables In short, it is a constant is variable to identify its special status, we give it the distinctive name parameter

Equation and identities In economics applications we may distinguish between three types of equation: definitional equation, behavioral equation, conditional equaition. Definitional equation sets up an identity between two alternate expressions that have exactly the same meaning (sign ≡ ‘identically equal to’) Behavioral equation may involve either human behavior such as consumption, production function, tax structure C=75 + Q Conditional equation states a requirement to be satisfied, for example in a model of equilibrium Qd = Qs MR = MC

Consept of sets Himpunan adalah suatu kumpulan atau gugusan dari sejumlah obyek Obyek yang mengisi atau membentuk sebuah himpunan disebut anggota atau elemen Obyek himpunan berupa benda, angka, huruf Himpunan disajikan dengan huruf A;B;C;D Obyek yang menjadi anggota himpunan disajikan dengan huruf a;b;c;d

NOTASI HIMPUNAN a A berarti obyek a adalah anggota/elemen himpunan A A B Berarti A merupakan himpunan bagian dari B A = B Berarti angota himpunan A juga merupakan anggota B A ≠ B Berarti himpunan A tidak sama dengan B

Penyajian Himpunan Cara daftar A = {1,2,3,4,5} Cara kaidah A= {x; 0< x <6} A= {x; 1≤ x ≤5}

Contoh penulisan Himpunan U = {0,1,2,3,4,5,6,7,8,9} Kesimpulan yang bisa ditarik adalah x U dimana 0 ≤ x ≤ 4 A = {0,1,2,3,4} B = {5,6,7,8,9} C = {0,1,2,3,4} A ≠ C, A ≠ B, dan B ≠ C

pada sebuah taman kanak-kanak sedang diadakan pelajaran berhitung, seorang guru mencoba menguji kepandaian anak-anak: Guru: ani, coba kamu hitung 1- 5 Ani: satu, dua, tiga, empat, lima Guru: pintar kamu ani, nia coba kamu hitung angka selanjutnya Nia: enam, tujuh, delapan, sembilan, Guru: pintar kamu nia, banu coba kamu lanjutkan hitungan setelah sembilan Banu: sepuluh, jack, queen, king dan,as bu Guru: ##&??&*\$

OPERASI HIMPUNAN Union (gabungan) A U B = { x; x € A atau x € B} Intersection (irisan) A ∩ B = { x; x € A atau x € B} Selisih antara A dengan B ditulis dengan notasi A – B, adalah himpunan yang beranggotakan obyek milik A yang bukan obyek B

Contoh Operasi Himpunan U = {1,2,3,4,5,6,7,8,9} P = {1,2,3,4,5} Q = {4,5,6,7,8} R = {6,7,8,9} P U Q = {1,2,3,4,5,6,7,8} P ∩ Q = {4,5} P – Q = {1,2,3}

TUGAS U = {1,2,3,4,5,6,7,8} A = {2,3,5,7} B = {1,2,3,4,7,8} A-B, B-A, A ∩ B, A U A

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