Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Ekonomi |
| Periode Ujian | : | April 2019 |
| Nomor Soal | : | 6 |
SOAL
Jika fungsi permintaan dinyatakan dalam persamaan \({Q_d} = 40 – 2P\), berapakah besarnya surplus konsumen (consumer surplus) pada harga Rp. 10?
- 83
- 97
- 100
- 127
- 131
| Diketahui | \({Q_d} = 40 – 2P\)
\(2P = 40 – {Q_d}\)
\(P = 20 – 0,5{Q_d}\) |
| Rumus yang digunakan | Consumer Surplus - \(Cs = \int\limits_{{P_d}}^P {f\left( P \right)\,dP} \)
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| Proses pengerjaan | Masukkan P=0 dan Q=0- Ketika P = 0
\(P = 20 – 0,5{Q_d}\)
\(0 = 20 – 0,5{Q_d}\)
\(0,5{Q_d} = 20\)
\({Q_d} = 40\) - Ketika Q = 0
\(P = 20 – 0,5{Q_d}\)
\(P = 20 – 0,5(0)\)
\(P = 20\) - Sehingga \(\left( {P,Q} \right) = \left( {20\,,\,\,40} \right)\)
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| Menggunakan rumus Consumer Surplus
\(Cs = \int\limits_{{P_d}}^P {f\left( P \right)\,dP} \)
\(= \int\limits_{10}^{20} {40 – 2P\,\,dP} \)
\(= \left. {40P – \frac{{2{P^2}}}{2}\,\,} \right|_{10}^{20}\)
\(= \left[ {40\left( {20} \right) – \frac{{2\left( {{{20}^2}} \right)}}{2}} \right] – \left[ {40\left( {10} \right) – \frac{{2\left( {{{10}^2}} \right)}}{2}} \right]\)
\(= \left[ {800 – 400} \right] – \left[ {400 – 100} \right]\)
\(= 400 – 300 = 100\) |
| Jawaban | c. 100 |
