oh god pls give me an A

A situation where there are multiple possible outcomes, and each outcome has a probability of happening

Lottery

For the lottery, the probabilities of all possible outcomes must add up to

100%

The average payoff you expect to receive, considering the probability of each outcome

Expected Value

Expected Value formula

• pi = probability of an outcome

• Xi = payoff/value of that outcome

Measures how risky or unpredictable a lottery is

Variance

Variance formula

• Higher variance = More risk (outcomes are more spread out)

• Lower variance = Less risk (outcomes are closer together)

The typical spread of outcomes around the expected value

Standard Deviation

Standard Deviation formula

SD=/Var

The average satisfaction or happiness you expect to get from a lottery

Expected Utility

Expected Utility formula

• pi = Probability of each outcome

• u(xi) = Utility received from that outcome

difference between EV and EU

EV

• Measures expected money

• Uses actual payoffs

EU

• Measures expected satisfaction

• Uses utility of payoffs

The St. Petersburg Paradox meaning

A lottery can have an infinite Expected Value (EV), but people are still NOT willing to pay an infinite amount to play

As you receive more money, each additional dollar gives you less additional satisfaction

Diminishing Marginal Utility of Money

Risk level that prefers certainty

Risk-averse → u(EV)>EU

Risk level willing to give up some potential earnings in exchange for certainty

Risk-averse → u(EV)>EU

Risk level that is indifferent between certainty and gamble

Risk-neutral → u(EV)=EU

Risk level that arises when an individual’s utility function is linear, meaning they are indifferent between receiving the expected value for sure and playing the lottery 

Risk-neutral → u(EV)=EU

Risk level that prefers the gamble

Risk-loving → u(EV)<EU

The amount of money a person is willing to give up to avoid the risk of a lottery

Risk Premium

In simpler terms: How much would you sacrifice to get a guaranteed amount instead of taking a gamble?

Risk Premium

Risk Premium formula

u(EV-RP)=EU

• EV = Expected Value (average monetary payoff)

• RP = Risk Premium (amount sacrificed to avoid risk)

• EU = Expected Utility (average satisfaction from the lottery)

The amount of money you would accept for sure instead of taking a gamble

Certainty Equivalent

In other words: How much guaranteed money would make you indifferent between receiving it and playing the lottery?

Certainty Equivalent

Certainty Equivalent formula

CE = EV - RP

• CE = Certainty Equivalent (guaranteed amount you'd accept)

• EV = Expected Value (average possible winnings)

• RP = Risk Premium (amount you're willing to sacrifice to avoid risk)

Measures how strongly a person dislikes taking risks

Arrow-Pratt Coefficient of Absolute Risk Aversion

Arrow-Pratt Coefficient of Absolute Risk Aversion formula

• u' = First derivative of utility (marginal utility)

• u'' = Second derivative of utility (how marginal utility changes)

meaning of Arrow-Pratt Coefficient of Absolute Risk Aversion

• Positive AP = Avoids risk

• Negative AP = Loves risk

• Zero AP = Neutral to risk

The area below the demand curve and above the price that consumers pay for the good

Consumer surplus

Consumer surplus formula

Willingness to pay − Actual price = Consumer Surplus

Consumer surplus → linear demand formula

CS=1/2 x Height x Base

• Height = (Maximum willingness to pay - Actual price)

• Base = Quantity

Consumer surplus → nonlinear demand formula

• P1 = Original (higher) price

• P2 = New (lower) price

• x(p) = Demand function

How much money we need to take away from or give to a consumer after a price change to keep them at the same level of happiness (utility) as before

Compensating variation

If the price decreases, what is the Compensating variation

• We take away some of their income to bring them back to their original happiness.

• The amount taken away = CV

If the price increases, what is the Compensating variation

• We give them additional income to bring them back to their original happiness

• The amount given = CV

How much money you need to GIVE or TAKE AWAY from a consumer BEFORE a price change to make them feel as happy as they would AFTER the price change

Equivalent variation

If the price decreases, what is the Equivalent variation

• We need to GIVE them extra money BEFORE the price decrease to make them equally happy as they would be after the decrease.

• EV = Extra money given.

If the price increases, what is the Equivalent variation

• We need to TAKE AWAY money BEFORE the price increase to make them as badly off as they would be after the increase.

• EV = Money taken away.

CV vs EV

CV = After the price change.

EV = Before the price change.

When are the three measures of welfare change are equal

WHEN income effects are zero

It means a change in income does NOT affect how much of a good the consumer buys

Zero Income Effect

When does zero income effect happen

• The good takes up a very small part of income

• The good has very low income elasticity

Describes how a firm transforms inputs (capital and labor) into output (goods or services)

Production Function

Production Function

q=f(K,L)

• q = quantity of output produced

• K = capital (machines, equipment, buildings)

• L = labor (workers)

• A = technology/productivity parameter

production function → Capital and labor combine multiplicatively to produce output. Both inputs contribute to production.

Cobb-Douglas

Cobb-Douglas production function

production function → Capital and labor are perfect substitutes. One input can replace the other.

Linear

Linear production function

q=aK+bL

production function → Capital and labor must be used in fixed proportions. Excess of one input cannot compensate for a shortage of the other.

Leontief (Fixed Proportions)

Leontief (Fixed Proportions) production function

q=A min{aK,bL}

production function → Additional capital increases output, but at a decreasing rate. Labor contributes linearly.

Diminishing Returns to Capital

Diminishing Returns to Capital production function

Measures how efficiently a firm uses its inputs (labor and capital) to produce output

Productivity of Inputs

The total output produced per unit of input

Average Product

Average output produced by each worker

Average Product of Labor (APₗ)

Average Product of Labor (APₗ) formula

APL = q / L

Average output produced by each unit of capital

Average Product of Capital (APₖ)

Average Product of Capital (APₖ) formula

APk = q / K

The additional output produced when one additional unit of an input is used, holding other inputs constant

Marginal Product

Marginal Product of Labor (MPₗ) formulas

Marginal Product of Capital (MPₖ) formulas

Relationship Between Average Product and Marginal Product

Marginal Product pulls Average Product toward itself

what happens when MP>AP

Marginal product pulls the average upward.

• AP is increasing

what happens when MP<AP

Marginal product pulls the average downward.

• AP is decreasing

what happens when MP=AP

Marginal product intersects average product at its highest point.

• AP is at its maximum

Explains how a firm can change the combination of labor (L) and capital (K) while maintaining the same level of output

Input Substitution

Explains how a firm can change the combination of labor (L) and capital (K) while maintaining the same level of output

Input Substitution

Represents different combinations of labor and capital that produce the same amount of output

Isoquant Curve

Isoquant Curve axis

X-axis = Labor (L); Y-axis = Capital (K)

Three characteristics of isoquant curves

Downward-slopping Convex to the origin Do not intersect

Why are isoquant curves are downward-sloping

More labor allows the firm to use less capital while maintaining the same output

Why are isoquant curves are convex to the origin

The rate at which inputs substitute for each other diminishes

Measures how much capital a firm can reduce when it increases labor by one unit, while keeping output constant

Marginal Rate of Technical Substitution

MRTS Function

• MPL = Marginal product of labor

• MPK = Marginal product of capital

As a firm continues substituting labor for capital, it needs to give up less and less capital for each additional unit of labor

Diminishing MRTS

MRTS level when very little capital can be replaced by additional labor

Low

MRTS level when smaller amounts of capital can be replaced

Moderate

MRTS level when large amounts of capital can be replaced by additional labor

High

The isoquant equation derived

Why Is MRTS Constant?

Because a and b are constants

Why does it mean MRTS is constant?

This means the firm can always substitute the same amount of capital for an additional unit of labor, regardless of its current input combination

aL<bK

Not enough labor → need more workers

aL>bK

Not enough capital → need more machines

aL=bK

Inputs are balanced → neither input is wasted

How a firm's total output changes when ALL inputs (labor and capital) are increased by the same proportion

Returns to Scale

Mathematical condition of IRS

Mathematical condition of DRS

Mathematical condition of CRS

Returns to scale → Output increases MORE than proportionally to inputs

Increasing Returns to Scale (IRS)

Returns to scale → Output increases LESS than proportionally to inputs.

Decreasing Returns to Scale (DRS)

Returns to scale → Output increases proportionally to inputs

Constant Returns to Scale (CRS)

Refers to improvements in a firm's production technology that allow it to produce MORE output using the SAME amount of inputs (labor and capital)

Technological Progress

Technological progress → Overall productivity increases. The firm produces more using the same inputs

General productivity improvement

Technological progress → Labor becomes more productive

Labor-enhancing progress

Technological progress → Capital becomes more productive

Capital-enhancing progress

General productivity improvement function

Labor-enhancing progress function

Capital-enhancing progress function

A firm wants to produce a certain amount of output while spending as little as possible

Cost Minimization

Shows combinations of labor (L) and capital (K) that cost the same amount

Isocost Line