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Economics Note

Chapter 1: Analyzing Economic Problems

Economics is the science that deals with the allocation of limited resources to satisfy unlimited human wants

That is why economics is often described as the science of constrained choice.

Three Key Analytical Tools

Constrained Optimization

Equilibrium Analysis

Comparative Statics

Positive and Normative Analysis

Chapter 2: Demand and Supply Analysis

2.1 Demand, Supply, and Market Equilibrium

2.2 Own-Price Elasticiyty of Demand 价格弹性

\[\begin{aligned} & \epsilon_{Q, P} = \frac{percentage\ change\ in\ quantity}{percentage\ change\ in\ price}\\ \end{aligned}\] \[\begin{aligned} & (Q的变化量相对于当下Q的比例)percentage\ change\ in\ quantity=\frac{\Delta Q}{Q} 100%\\ \end{aligned}\] \[\begin{aligned} & (P的变化量相对于当下的P的比例)percentage\ change\ in\ price=\frac{\Delta P}{P} 100%\\ \end{aligned}\] \[\begin{aligned} & \epsilon_{Q,P} =\frac{\Delta Q}{\Delta P}\frac{P}{Q} \end{aligned}\] \[\begin{aligned} & \epsilon_{Q,P} =\frac{\Delta Q}{\Delta P}\frac{P}{Q} = \frac{-5}{2}\frac{10}{50} = -0.5 \end{aligned}\]

Elastic along specific demand curves

\[\begin{aligned} & \epsilon_{Q,P} =\frac{\Delta Q}{\Delta P}\frac{P}{Q} = -b\frac{P}{Q} \end{aligned}\]

2.3 Other Elasticities

\[\begin{aligned} & \epsilon_{Q, I}=\frac{\Delta Q}{\Delta I}\frac{I}{Q} \end{aligned}\] \[\begin{aligned} & \epsilon_{Q_i, P_j} = \frac{\Delta Q_{i}}{\Delta P_j}\frac{P_j}{Q_i} \end{aligned}\]

但是，《经济学人》也不得不考虑道德力量。确实有人试图就“经济人”的行为建立一种抽象的科学，经济人不受道德的影响，谨慎而积极地追求金钱利益，但机械地和自私地。但是它们没有成功，甚至没有完全执行;因为他们从来没有真正把经济人看作完全自私的人。最可靠的人莫过于有经济头脑的人，他为了养家糊口而无私地吃苦耐劳、牺牲牺牲;他的正常动机一直被默认为包括家庭感情在内。但是，如果把这些动机也包括在内，为什么不把所有其他的利他动机也包括在内呢?到目前为止，任何阶级、任何时间、任何地点的所有其他利他动机的行为都是一致的，因此可以归结为普遍规律。”

Chapter 3: Consumer Preferences and the Concept of Utility

3.1 Representation of preferences

3.2 Utility Functions

\[\begin{aligned} & MU = \frac{dU}{dy} \end{aligned}\] 
因为这个不需要化简单位，所以在图像上，marginal utility就是在utility function函数上某一点的切线斜率

Preferences with multiple goods: Marginal Utility, Indifference Curves and the marginal rate of substitution

3.3 Special Preferences

4 Consumer Choice

4.1 The Budget constraint

4.2 Optimal Choice

\[\begin{aligned} & \mathop{max}_{(x, y)} U(x, y) \\ & subject\ to:\ P_{x}x + P_{y}y \leq I \end{aligned}\]

\[\begin{aligned} & \mathop{min}_{(x, y)} expenditure = P_{x}x + P_{y}y \\ & subject\ to:\ U(x, y) = U_{2} \end{aligned}\]

Chapter 4: Appendix 1: The Mathematics of Consumer Choice

\[\begin{aligned} & \text{Assume current funtcion is z = f(x, y) and } \phi(x, y)=0 \\ & \text{goal is to maximize z while preserving } \phi(x, y) = 0 \\ & \text{Lagranian Function will be defined as } F(x, y, \lambda) = f(x, y) + \lambda \phi(x, y)\\ \end{aligned}\] \[\begin{aligned} & F'_{x} = f'_{x}(x, y) + \lambda {\phi}'_{x}(x, y) = 0 \\ & F'_{y} = f'_{y}(x, y) + \lambda {\phi}'_{y}(x, y) = 0 \\ & F'_{\lambda} = {\phi}(x, y) = 0 \\ & \text{也就是对这三个值分别求导等于0，必须找到这样一个combination就可以了} \end{aligned}\] \[\begin{aligned} & \mathop{max}_{(x, y)} U(x, y) \\ & subject\ to:\ P_{x}x + P_{y}y \leq I \end{aligned}\]

\[\begin{aligned} & \frac{MU_x}{MU_y} = \frac{P_x}{P_y} \\ & P_{x}x + P_{y}y = I \\ \end{aligned}\]

Chapter 5: The theory of Demand

5.1 Optimal Choice and demand

5.1 Change in the price of good: Substitution Effect and Income Effect

THE SUBSTITUTION EFFECT

THE INCOME EFFECT

When goods are not normal

5.3 Change in the price of a good: The concept of consumer surplus消费者盈余

Understanding consumer surplus from the optimal choice diagram: compensating variation and equivalent variation

Market Demand

4.3 Consumer Choice With Composite Goods

Application: Coupons and cash sbusidies

Applicatio: Joining a club

Application: Borrowing and Lending

Application: Quantity Discounts

Chapter 4: Appendix 2: The time value of the money

Future value and present value

Net Present Value

Presnet value, future value and the optimal consumption choice problem

5.5 The Choice of labor and leisure

As wages rise, leisure first decreases, then increases

The Backward-bending supply of labor

Chapter 15: Risk and Information

15.1: Describing Risky Outcomes

\[\begin{aligned} \text{Expected Value} = & \text{probability of A} \times \text{payoff iff A occurs} \\ & \text{probability of B} \times \text{payoff iff B occurs} \\ & \text{probability of C} \times \text{payoff iff C occurs} \\ \end{aligned}\]

15.2: Evaluating Risky Outcomes

15.3 Bearing and eliminating risk

When would a risk-averse person choose to eliminate risk? The demand for insurance

Asymmetric Information: Moral Hazard and Adverse Selection

Pay for performance as a response to maral hazard and adverse selection

Chanpter 6: Input and Production Functions

6.1 Introduction to inputs and production functions

6.2 Production Functions With A Single Input

6.3: Production Functions with more than one input

Isoquants

Marginal Rate of Technical Substitution

6.4 Substitutability among Inputs

Elasticity of Substitution

\[\begin{aligned} \text{The elascity of substition} \\ \sigma &= \frac{\text{percentage change in capital-labor ratio}}{\text{percentage change in } MRTS_{L,K}}\\ &= \frac{\% \Delta \frac{K}{L}}{\% \Delta MRTS_{L,K}} \end{aligned}\]

Special Production Functions

Linear Production Function(Perfect Substitute)

Fixed-properties production function(Perfect Complements)

Cobb-Douglas production function

Constant elasticity of substitution production function

6.5 Returns to Scale

\[\text{Return to scale } = \frac{\% \Delta (quantity\ of\ output)}{\% \Delta (quantity\ of\ all\ inputs)}\]

6.6 Technological Progress

Chapter 7: Costs and Cost minimization

7.1 Cost Concepts for decision making

Economic Versus Accounting Costs

Chapter 8: Cost Curves(Seriously, do u suprise?)

8,1 Long-Run Cost Curves

How does the long run total cost curve shift when input prices change

What happens when all input prices change proportionately

Long-Run average and Maginal Cost Curves

· Index ·
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