戰昇的部落格

今天是第四週課程內容是關於需求，內容涵蓋效用、效用極大化與預算限制，以及需求函數的推導。

一、效用（Utility）

1. 效用函數的建立

- 在商品空間中構建效用函數，將消費組合指派為一個實數，用於偏好的數值化表示。

- 效用函數需符合偏好的秩序轉換原則：

2. 效用的序數性

- 效用函數僅描述消費者對不同組合的偏好順序，而非對組合滿意度的絕對衡量。

- 任意單調遞增轉換的效用函數均可表示相同偏好關係。

3. 無差異曲線（Indifference Curve）

- 根據效用水準繪製的曲線，表示相同滿意度的消費組合集合。

二、效用極大化與預算限制（Utility Maximization under Budget Constraint）

1. 效用極大化模型

- 消費者以滿足預算限制的情況下，追求效用極大化：

2. 拉格朗日方法與最優條件

- 將問題轉化為拉格朗日方程

- 最優條件需滿足的方程式

3. 主觀與客觀機會成本的平衡

 最優組合需滿足的情況

三、需求函數（Demand Function）

1. 需求函數的推導

- 從最優條件與預算限制推導需求函數，例如 Cobb-Douglas 

2. 需求函數的特性

- 正常財：需求量隨收入增加而增加。

- 劣等財：需求量隨收入增加而減少。

- 價格效果：需求量隨商品價格增加而減少。

3. 應用：稅制比較

- 比較從價稅與整筆稅對消費者效用的影響，得出整筆稅較優的結論。

Today’s Week 4 lecture focused on Demand, covering topics such as utility, utility maximization under budget constraints, and the derivation of demand functions.

A. Utility

1. Construction of the Utility Function

- A utility function is constructed in the commodity space, assigning a real number to each consumption bundle to represent preferences numerically.

- The utility function must adhere to the principle of preference order transformation:

2. Ordinal Nature of Utility

- A utility function only describes the ranking of preferences among bundles, not the absolute level of satisfaction.

- Any monotonic transformation of a utility function can represent the same preference relations.

3. indifference Curve

- Indifference curves are drawn based on utility levels, representing sets of consumption bundles with the same satisfaction level.

B. Utility Maximization under Budget Constraints

1. Utility Maximization Model

- Consumers aim to maximize utility subject to budget constraints:

2. Lagrangian Method and Optimality Conditions

- The problem is reformulated into a Lagrangian equation.

- The optimal conditions must satisfy the following equations:

- (Insert equations for optimality conditions here)

3. Balancing Subjective and Objective Opportunity Costs

- The optimal consumption bundle satisfies:

C. Demand Function

1. Derivation of the Demand Function

- The demand function is derived from the optimality conditions and budget constraints, such as in the Cobb-Douglas case.

2. Characteristics of Demand Functions

- Normal Goods: Demand increases with income.

- Inferior Goods: Demand decreases with income.

- Price Effect: Demand decreases as the price of a good increases.

3. Applications: Tax Scheme Comparison

- A comparison between ad valorem taxes and lump-sum taxes demonstrates that lump-sum taxes are more favorable for consumers.