Presentasi sedang didownload. Silahkan tunggu

Presentasi sedang didownload. Silahkan tunggu

Diferensial Fungsi Majemuk - Diferensial Parsial - Diferensial Total - Chain rule - dll.

Presentasi serupa


Presentasi berjudul: "Diferensial Fungsi Majemuk - Diferensial Parsial - Diferensial Total - Chain rule - dll."— Transcript presentasi:

1 Diferensial Fungsi Majemuk - Diferensial Parsial - Diferensial Total - Chain rule - dll

2 Diferensial Parsial Diferensial Total

3 High Order Partial Derivatives Fungsi dengan lebih dari satu variabel bebas juga dapat diturunkan lebih dari satu kali Turunan parsial z = f (x,y)  kalau kontinyu dapat mempunyai turunannya sendiri.  empat turunan parsial : Dapat dilambangkan f xx, f xy, f yx, dan f yy f xy = f yx

4 Partial derivatives Cobb-Douglas production function (  +  =1) Q = 96K 0.3 L 0.7

5 Techniques of partial differentiation Market model

6 Geometric interpretation of partial derivatives Market model

7

8 QS1S1 DPDP S0S0 QS DPDP D1D1

9 Q S0S0 D1D1 D0D0 P Q0Q0 Q1Q1 QS0S0 DPDP S1S1

10 National-income model Y = C + I 0 + G 0 C = a + b(Y-T); b = MPC (a > 0; 0 < b < 1) T=d+tY; t = MPT (d > 0; 0 < t < 1) Y=( a-bd+I+G)/(1-b+tb) C=(b(1-t)(I+G)+a-bd)/ (1-b+tb) T=(t(I+G)+ta+d(1-b))/ (1-b+tb)

11 Input-output model ∂x 1 /∂d 1 = b 11

12 Note on Jacobian Determinants Use Jacobian determinants to test the existence of functional dependence between the functions /J/ Not limited to linear functions as /A/ (special case of /J/ If /J/ = 0 then the non-linear or linear functions are dependent and a solution does not exist.

13 Total Differentials

14 Diferensial Total

15 Let Utility function U = U (x 1, x 2, …, x n ) Differentiation of U wrt x 1..n  U/  x i is the marginal utility of the good x i dx i is the change in consumption of good x i

16 Finding the total derivative from the differential Given a function y = f (x 1, x 2, …, x n ) Total differential dy is: Total derivative of y with respect to x 2 found by dividing both sides by dx 2 (partial total derivative)

17 Chain rule (kaidah rantai) This is a case of two or more differentiable functions, in which each has a distinct independent variable. where z = f(g(x)), i.e., z = f(y), i.e., z is a function of variable y and y = g(x), i.e., y is a function of variable x If R = f(Q) and if Q = g(L)

18 Kaidah Rantai z t xy Pohon rantai

19 Kaidah Rantai Kalau w = w(x,y,z) dan x = x(u,v), y = y(u,v), dan z = z(u,v), maka pohon rantai : w y v z u x

20 Kalau z = z(x,y), dan x = x(s), y = y(s), dan s = s(u,v), maka pohon rantai menjadi : z x u s y v


Download ppt "Diferensial Fungsi Majemuk - Diferensial Parsial - Diferensial Total - Chain rule - dll."

Presentasi serupa


Iklan oleh Google