Managerial Economics Poblems

Soal : a researcher estimated that the price elasticity of demand for automobiles in the United States is – 1.2, while the income elasticity of demand is 3.0. Next year, U.S. automakers intend to increase the average price of automobiles by 5 percent, and they expect consumers; disposable          income to rise by 3 percent. (a) If sales domestically produced automobiles are 8 million this          year, how many automobiles do you expect U.S. automakers to sell next year ? (b). By how          much should domestic automakers increase the price of automobiles if they wish to increase sales by 5 percent next year ?

Diketahui :  ϵd = -1.2
 ϵi = +3
%ΔP = +5%
%ΔI = +3%
Jawab :

a)

ϵd

=

%ΔQ
%ΔP
-1,2

=

%ΔQ
5%
%ΔQ = – 6%
ϵi

=

%ΔQ
%ΔI
3

=

%ΔQ
3%
%ΔQ = + 9%

Total %ΔQ =     -6%   +   9%     =     3%

Jadi jumlah mobil yang harus dijual di tahun depan (asumsi ceteris paribus) adalah

= 8.000.000 x ( 100% + 3% )

= 8.000.000 x 103%

= 8.240.000 mobil

b) Jika produsen ingin meningkatkan penjualan 5% ditahun depan

5%  =   x  +  9%

X     = – 4%

ϵd

=

%ΔQ
%ΔP
-1,2

=

-4%
%ΔP

%ΔP

=

-4%
-1,2

%ΔP

= 3,3%

Soal : The management of the Mini Mill Steel Company estimated the following elasticities for a special type of steel : Ep = – 2, EI= 1, and Exy = 1,5, where X refers to steel and Y to  aluminum. Next year, the firm would like to increase the price of the steel it sells by 6 percent. The management forecasted that income will rise by 4 percent next year and that the price of aluminum will fall by 2 percent.

(a) If the sales this year are 1,200 tons of the steel, how             many tons can the firm expect to sell next year ?

(b) By what percentage must the firm change the price of steel to keep its sales at 1,200 tons next year ?

 

Diketahui :

Ep = -2
EI = 1
Exy = 1,5
X = steel
Y = alumunium
Exy artinya perubahan Quantity X terhadap   Price Y
Exy

=

%ΔQx
%ΔPy

Jawab :

a)      Sales X tahun ini = 1.200 ton, berapa ton yang bisa dijual tahun depan?

Elastisitas demand

ϵp

=

%ΔQ
%ΔPx
-2

=

%ΔQ
6%

%ΔQ

=

6%   x (-2)

%ΔQ = -12%

Elastisitas terhadap barang Y

Exy

=

%ΔQx
%ΔPy
1,5

=

%ΔQ
-2%
%ΔQ = –   3%

Elastisitas Income

ϵi

=

%ΔQ
%ΔI
1

=

%ΔQ
4%
%ΔQ = +   4%

Total ΔQ  = -12%   –  3%   +   4%    =    – 11%

Jadi… jumlah penjualan tahun depan adalah     1.200   x    ( 100% – 11% )  =   1.200 x 89% =  1.068 ton

b)      Berapa persen perubahan harga Steel yang harus ditetapkan oleh produsen agar penjualannya tetap pada level 1.200 ton?

 

ΔQ  =    X%   –  3%   +   4%

0     =    X%   –  3%   +   4%

X%  =     – 1%

ϵp

=

%ΔQ
%ΔPx
-2

=

-1%
X%

X

=

0,5%

%ΔP = 0,5% (harga   dinaikkan sebesar 0,5%)

SOAL :Suppose the own price elasticity of demand for good X is  – 2, its income elasticity  is  3, its advertising elasticity  is  4, and its cross price elasticity of demand between  it and good Y is – 6. Determine how much the consumption of this good will change if:

                  a. The price of good X increases by 5%

                  b. The price of good Y increases by 10%

                  c. Advertising decreases by 2 %

                  d. Income falls by 3%

 

 

Jawab :

ϵp = -2
ϵi = +3
ϵA = +4
ϵxy = -6

a)      %ΔPx = +5%

ϵpx

=

%ΔQ
%ΔPx
-2

=

%ΔQ
5%
%ΔQ = -10%

b)      %ΔPy = +10%

 

ϵxy

=

%ΔQ
%ΔPy
-6

=

%ΔQ
10%
%ΔQ = -60%

 

 

c)       %ΔPadv = -2

 

ϵA

=

%ΔQ
%ΔPa
4

=

%ΔQ
– 2 %
%ΔQ = -8%

 

d)      %ΔI = -3

 

ϵI

=

%ΔQ
%ΔI
3

=

%ΔQ
– 3 %
%ΔQ = -9%

 

 

 

SOAL : The ACME Corporation determines that at current prices, the demand for its computer chips has a price elasticity of – 2 in the short run. The price elasticity of its disc drivers is  – 1.  a). If  ACME decides to raise the price of both products by 10%, what will happen to its sales? To its sales revenue?  b) Can you tell from the above information which product will generate more revenue? If yes, which one?

 

 

Jawab :

 

X = Chips

Y = Disc

 

ϵpx = -2

ϵpy = -1

%ΔPx = +10%

ϵpx

=

%ΔQ
%ΔPx
-2

=

%ΔQ
10 %
%ΔQ = -20%

(karena demand-nya elastis, maka sales Chips turun sebesar 20%)

 

ϵpy

=

%ΔQ
%ΔPy
-1

=

%ΔQ
10 %
%ΔQ = -10%

(karena demand-nya elastis, maka sales Disc turun sebesar 10%)

 

 

Sales revenue = TR = PQ

DTR        = [(100%+10%) P1  X (100%-20%)Q1 ] – P1Q1

DTR        = (1.1P1 )(0.8Q1 ) – P1Q1

= –0.12P1Q1            (atau turun sebesar 12%)

 

Sales revenue Disc tidak berubah, karena elastisitas demand-nya -1

 

Product yang menghasilkan paling banyak revenue tidak dapat diketahui, karena Price dan Quantity masing-masing product tidak diketahui.

 

 

 

SOAL : Y = X   +      4 X²   –  0,2 X³

Ditanya :

 

a)      APx  

APx

=

Y

X

APx

=

X     +    4 X²   –    0,2 X³

X

APx = 1     +    4 X  –    0,2 X²

 

b)      MPx

MPx = Y’ =   1   +   8X  –    0,6 X²

 

c)       TPmax = MPx = 0

 

0   =   1   +   8X  –    0,6 X²

0   =  –  0,6  X²  +   8X  +   1

 

Rumus Persamaan Kuadrat untuk mencari X1 dan X2 :

                      

 Rumus Persamaan Kuadrat

 
Rumus Persamaan Kuadrat

Dari persamaan kuadrat   –  0,6  X²  +   8X  +   1

Didapat :              a              =  -0,6

                                b             =  8

                                c              =   1

Setelah dimasukkan ke dalam Rumus Persamaan Kuadrat , didapat nilai X1 = – 0,125   dan X2 = 13,45

Yang digunakan adalah X yang positif , yaitu X2 = 13,45

Y             =             X   +    4 X²   –  0,2 X³

                =             13,45 + 4 (13,45) ² – 0,2 (13,45) ³

                =             250,422

 

Daerah Rasional ->   AP = MP

AP                                          =                             MP

1 + 4 X – 0,2 X²   =  1 + 8X – 0,6 X²

8X – 4X – 0,6X² + 0,2 X² = 0

4X – 0,4X²                            = 0

4                                              = 0,4 X

X                                             = 4/0,4

X                                             = 10

 

Jadi daerah rasional :     10 <  X  <  13,45 (Stage II)

TP max pada saat X = 13,45

 

Stage of Production Function

Stage of Production Function

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