OPTIMASI EKONOMI

OLEH:FIEN ZULFIKARIJAH

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

TEORI PERUSAHAAN

• Perusahaan adalah kombinasi dari berbagai sumberdaya

• Tujuan perusahaan adalah memperoleh keuntungan

• Adanya ketidakpastian menyebabkan perusahaan bergeser untuk memaksimalkan kekayaan /nilai

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Pengertian nilai• Nilai perusahaan adalah nilai sekarang (PV) darialiran

kas suatu perusahaan yang diharapkan akan diterima di masa yang akan datang

• Present value (PV) of an amount (FV) to be received at the end of “n” periods when the per-period interest rate is “i”:

PVFV

i n1

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Present Value of a Series

• Present value of a stream of future amounts (FVt) received at the end of each period for “n” periods:

PVFV

i

FV

i

FV

inn

11

221 1 1. . .

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Net Present Value• Suppose a manager can purchase a stream of

future receipts (FVt ) by spending “C0” dollars today. The NPV of such a decision is

NPV CFV

i

FV

i

FV

inn

011

221 1 1. . .

NPV < 0: RejectNPV > 0: Accept

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

KENDALA DALAM TEORI PERUSAHAAN

• Accounting Profits– Total revenue (sales) minus dollar cost of

producing goods or services– Reported on the firm’s income statement

• Economic Profits– Total revenue minus total opportunity cost

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

• Accounting Profits– Total revenue (sales) minus dollar cost of

producing goods or services– Reported on the firm’s income statement

• Economic Profits– Total revenue minus total opportunity cost

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Opportunity Cost

• Accounting Costs– The explicit costs of the resources needed to

produce produce goods or services– Reported on the firm’s income statement

• Opportunity Cost– The cost of the explicit and implicit resources

that are foregone when a decision is made• Economic Profits– Total revenue minus total opportunity cost

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Market Interactions• Consumer-Producer Rivalry– Consumers attempt to locate low prices, while

producers attempt to charge high prices• Consumer-Consumer Rivalry– Scarcity of goods reduces the negotiating power of

consumers as they compete for the right to those goods

• Producer-Producer Rivalry– Scarcity of consumers causes producers to compete

with one another for the right to service customers• The Role of Government– Disciplines the market process

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Firm Valuation• The value of a firm equals the present value of

all its future profits– PV = S pt / (1 + i)t

• If profits grow at a constant rate, g < i, then:– PV = po ( 1+i) / ( i - g), po = current profit level.

• Maximizing Short-Term Profits– If the growth rate in profits < interest rate and both

remain constant, maximizing the present value of all future profits is the same as maximizing current profits.

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

• Control Variables– Output– Price– Product Quality– Advertising– R&D

• Basic Managerial Question: How much of the control variable should be used to maximize net benefits?

Marginal (Incremental) Analysis

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Net Benefits

• Net Benefits = Total Benefits - Total Costs• Profits = Revenue - Costs

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Marginal Benefit (MB)

• Change in total benefits arising from a change in the control variable, Q:

MB = DB / DQ• Slope (calculus derivative) of the total benefit

curve

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Marginal Cost (MC)

• Change in total costs arising from a change in the control variable, Q:

MC = DC / DQ• Slope (calculus derivative) of the total cost

curve

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

Marginal Principle

• To maximize net benefits, the managerial control variable should be increased up to the point where MB = MC

• MB > MC means the last unit of the control variable increased benefits more than it increased costs

• MB < MC means the last unit of the control variable increased costs more than it increased benefits

Michael R. Baye, Managerial Economics and Business Strategy, 3e. ©The McGraw-Hill

Companies, Inc. , 1999

The Geometry of Optimization

Q

Benefits & CostsBenefits

Costs

Q*

B

CSlope = MC

Slope =MB

MAKSIMISASI NILAI PERUSAHAAN

TUJUAN POKOK PERUSAHAAN ADALAH MEMAKSIMUMKAN NILAI

PERUSAHAAN

nNILAI = ∑ LABA t=1 (1 + I)²

nNILAI = ∑ TOTAL REVENUE – TOTAL COST t=1

METODE PENYAJIAN HUBUNGAN EKONOMI

TR = F(Q) TR = PxQ

JIKA P = 150, MAKA:

TR = 150Q

MODEL TABEL DAN GRAFIKQ TR

1 150

2 300

3 450

4 600

5 750

6 900

1 2 3 4 5 60

100

200

300

400

500

600

700

800

900

1000

QTR

HUBUNGAN ANTARA NILAI TOTAL, RATA-RATA DAN MARGINAL

A. HUBUNGAN ANTARA NILAITOTAL DANMARGINAL

Q LABA TOTAL LABA MARGINAL

LABA RATA-RATA

1 0 - -

2 19 19 19

3 52 33 26

4 93 41 31

5 136 43 34

6 175 39 35

7 210 35 35

8 217 7 21

9 208 -9 26

B. HUBUNGAN ANTARA NILAI RATA-RATA DENGAN MARGINALJIKA NILAI MARGINAL > NILAI RATA-RATA, MAKA NILAI RATA-RATA SEDANG NAIK

C. KALKULUS DIFFERENSIAL

Y =f(X)

marginal Y = dY/dX

dY = Y2 – Y1/X2 –X1

D. KAIDAH-KAIDAH PENURUNAN SUATU FUNGSI1. Kaidah konstanta

dY/dX = 02. Kaidah pangkat

Y = aX² -- dY/dX = 2.aX

3. Kaidah penjumlahan dan selisih

U = g(X) -- V = h(X)

Y = U + V

dY/dX = dU/dX + dV/dX Y = 2X² + X³

4. Kaidah perkalian

Y = U.V

dY/dX = U dV/dX + V dU/dX

4. Kaidah perkalian

Y = U.V

dY/dX = U dV/dX + V dU/dX

contoh:

Y = 3X²(3-X)

dY/dX = 3X²(dV/dX) + (3-X) (dU/dX)

= 3X²(-1) + (3-X) (6X)

= 3X² + 18X -6X² = 18X – 9X²

5. Kaidah hasil bagi

Y = U/V

dY/dX = V dU/dX - U dV/dX

V²

contoh:

Y = 2X – 3

6X²

dY/dX = 6X².2 – (2X- 3) 12X

36X

= 12X² - 24X² + 36X

36X

= 36X - 12X²

3X³

6. Kaidah rantai

Y = 2U- U² dan U= 2X³

langkah 1: dY/dU = 2 – 2U

mensubstitusikan nilai U:

dY/dX = 2 – 2(2X³)

= 2- 4X³

langkah 2:

dU/dX = 6X²

langkah 3:

dY/dX = dY/dU x dU/dX

= (2 – 4X³) 6X²

= 12X² - 24X

PENGGUNAAN TURUNAN UNTUK MEMAKSIMUMKAN/MEMINIMUMKAN FUNGSI

Contoh:

∏ = -10.000 + 400Q – 2Q²

d ∏/dQ = 400 – 4Q

= 400 – 4Q = 0

Q = 400/4 = 100

Turunan fungsi ditunjukkan oleh nilai marginalnya, fungsi dikatakan maksimum atau minimum jika marginalnya sama dengan nol

Jadi keuntungan maksimal sebesar !0.000, pada saat Q = 100 unit

Jumlah produksi BEP pada saat:

∏ = -10.000 + 400Q – 2Q²

∏ = -5.000 + 200Q – Q²

∏ = Q² - 200Q + 5000

Menggunakan rumu ABC:

Q = -b ± Vb² - 4ac

2a

Q1 = -200 ± V200² - 4x5000 = 200+141 = 170,5 = 171

2 2

Q2 = -200± V200² - 4x5000 = 200 – 141 = 29,5 = 30

2 2

BEP terjadi pada saat Q= 30 dan Q=171

Laba sebagai output

10000

30 s 100 10000

jadi

PEMBEDAAN NILAI MAKSIMUM DAN MINIMUM

Contoh:

∏ = a – bQ + cQ² - dQ³

turunan pertama:

d ∏ /dQ = -b +2CQ – 3dQ²

turunan kedua

d² ∏/dQ² = 2C – 6dQ

Konsep turunan kedua digunakan untuk membedakan nilai maksimum dan minimum dari suatu fungsi Jika turunan kedua negatif titik yang ditentukan

maksimum Jika turunan kedua positif titik yang ditentukan minimum

Contoh:

∏ = 3000 – 2400Q + 3500Q² - 8,333Q³

turunan pertama:

d ∏ /dQ = -2400 +700Q – 25Q²

turunan kedua

d² ∏/dQ² = 700 – 50Q

pada tingkat output Q=4:

d² ∏/dQ² = 700 – 50(4) = 500 laba minimal

pada tingkat output Q=24:

d² ∏/dQ² = 700 – 50(24) = -500 laba maksimal

PENGGUNAAN TURUNAN UNTUK MEMAKSIMUMKAN SELISIH ANTARA2 FUNGSI

Contoh:

TR = 41,5Q – 1,1Q²

TC = 150 + 0,5Q²

T ∏ = TR – TC

= 41,5Q – 1,1Q² - (150 + 0,5Q ²)

= 41,5Q – 1,1Q² - 150 - 0,5Q ²

= -150 + 31,5Q – 0,06Q ²

turunan pertama:

d ∏ /dQ = 31,5 – 1,2Q – 0,06Q²

turunan kedua

d² ∏/dQ² = 1,2 – 0,12Q