Chapter 10 Functional Programming

Read:

• https://bookdown.org/rdpeng/RProgDA/functional-programming.html

• http://adv-r.had.co.nz/Functional-programming.html

Quiz 2 from https://adv-r.hadley.nz/functions.html

Cobb-Douglass效用函數： $$U(x,y,\alpha,\beta)=x^{\alpha}y^{\beta}$$ 1. 設計一個函數util_cobb_douglous(x,y,a,b)其input值如上表示，output值為numeric class效用水準。 $$U(\mathbb{X},\mathbb{\gamma})=\prod_{i=1}^n x_i^{\gamma_i},$$ 其中 $$\begin{array}{lcl} \mathbb{X}=\begin{bmatrix} x_1\\ x_2\\ \vdots \\ x_n \end{bmatrix},\ \mathbb{\gamma}=\begin{bmatrix} \gamma_1\\ \gamma_2\\ \vdots \\ \gamma_n \end{bmatrix} \end{array}$$

2. 設計util_cobb_douglous(x,g)其input值x及g均為numeric vector，output值為numeric class效用水準。

3. 設值一個泛函函數util_cobb_douglass_class()，使得下面最後一行會得到TRUE。

g <- c(0.1,0.3,0.4)
x <- c(1,3,10)
util_cobb_douglous_g <- util_cobb_douglass_class(g)
util_cobb_douglous_g(x) == util_cobb_douglous(x,g)