Microeconomics: Budget Lines and Demand
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Questions and Answers

What is the maximum amount of X that can be purchased if the income is $200 and the price of X is $5?

  • 20 units
  • 50 units
  • 40 units (correct)
  • 30 units

If a person buys one unit of X, how many units of Y can they purchase with the remaining income?

  • 22 units
  • 16 units
  • 20 units
  • 18 units (correct)

What does the slope of the budget line represent?

  • Total income
  • Total expenditure on X
  • Relative price of Y
  • Price of X over the price of Y (correct)

If the price of X increases, what effect does it have on the budget line?

<p>Shifts the line inward (B)</p> Signup and view all the answers

How does an increase in income affect the budget line?

<p>Shifts the line upward (C)</p> Signup and view all the answers

What happens to the budget line if the price of Y decreases?

<p>It becomes flatter (B)</p> Signup and view all the answers

What represents the intercept of the budget line on the Y-axis?

<p>Income divided by PY (C)</p> Signup and view all the answers

If a person receives a gift certificate of $20 for purchasing X, how does this affect their budget?

<p>Increases income overall (B)</p> Signup and view all the answers

What does the variable Ed represent in the context of elasticity?

<p>Price Elasticity of Demand (D)</p> Signup and view all the answers

If the price elasticity of demand is -1.14, what does this imply about quantity demanded in response to a price increase?

<p>Quantity will decrease by 1.14 percent for every one percent increase in price. (C), Quantity will decrease by 14 percent for every ten percent increase in price. (D)</p> Signup and view all the answers

In the demand function Q = aP - b, what do the constants a and b represent?

<p>Slope of the demand curve and fixed quantity sold, respectively. (C)</p> Signup and view all the answers

What happens to TOTAL REVENUE if the price rises and the price elasticity of demand is greater than 1?

<p>Total revenue decreases. (C)</p> Signup and view all the answers

What is the significance of taking the natural logs of both sides in the function ln Q = ln2 – 3ln P?

<p>It allows for the calculation of derivatives. (C)</p> Signup and view all the answers

In the equation dQ/dP, if Q = 2P - 3, what is the derivative of Q with respect to P?

<p>4 (A)</p> Signup and view all the answers

How does the coefficient of the variable in a logarithmic demand function relate to elasticity?

<p>It directly provides the value of elasticity. (D)</p> Signup and view all the answers

If a demand curve is perfectly inelastic, what would be the value of price elasticity of demand?

<p>0 (B)</p> Signup and view all the answers

What do constraints in a constrained optimization problem primarily represent?

<p>Restrictions or limits imposed on the decision maker (B)</p> Signup and view all the answers

Which term refers to the incremental impact of one additional unit of an independent variable on a dependent variable?

<p>Marginal cost (D)</p> Signup and view all the answers

What characterizes a state of equilibrium in a market?

<p>A condition that persists if no external factors change (A)</p> Signup and view all the answers

What is the primary use of comparative statics analysis?

<p>Analyzing the effects of a change in an exogenous variable (B)</p> Signup and view all the answers

Which statement correctly defines reservation price?

<p>The price at which a person is indifferent between acting or not acting (D)</p> Signup and view all the answers

In the context of a perfectly competitive market model, what does allocative efficiency aim to maximize?

<p>Social welfare (A)</p> Signup and view all the answers

What happens to the market when it is out of equilibrium?

<p>Exogenous factors prompt a return to equilibrium (A)</p> Signup and view all the answers

What does marginal reasoning in constrained optimization help determine?

<p>The effect of decision variables on the objective function (B)</p> Signup and view all the answers

What is the effect on utility when additional X is added while Y decreases?

<p>Utility will decrease due to the negative impact of decreasing Y. (B)</p> Signup and view all the answers

What does the Marginal Rate of Substitution (MRSx,y) represent?

<p>The rate at which a consumer is willing to give up Y in exchange for an additional unit of X. (D)</p> Signup and view all the answers

Which of the following statements about the MRSx,y for a linear utility function is true?

<p>The MRSx,y remains constant regardless of the quantities of X and Y consumed. (D)</p> Signup and view all the answers

In the utility function U(x, y) = 3x + y, what is the marginal utility of Y?

<p>1 (C)</p> Signup and view all the answers

For the utility function U = x^2 + y^2, how does the marginal utility of x behave?

<p>It increases as more x is consumed. (A)</p> Signup and view all the answers

Is the 'more is better' assumption satisfied for the utility function U = 3x + y?

<p>Yes, because both marginal utilities are always positive. (C)</p> Signup and view all the answers

What happens to MRSx,y as one moves along an indifference curve for the utility function U = x^2 + y^2?

<p>It diminishes as the consumer substitutes x for y. (C)</p> Signup and view all the answers

What is the marginal utility of x in the utility function U = x^2 + y^2?

<p>2x (A)</p> Signup and view all the answers

What does consumer equilibrium imply regarding the budget line and the highest indifference curve?

<p>The highest indifference curve is tangential to the budget line. (A)</p> Signup and view all the answers

Which equation represents the equality between marginal utility and price at consumer equilibrium?

<p>MU_X/PX = MU_Y/PY (A)</p> Signup and view all the answers

What condition must be satisfied for a consumer to maximize their total utility?

<p>The ratio of marginal utilities of the goods must equal the relative price ratio. (D)</p> Signup and view all the answers

In the constrained maximization problem, what does the Lagrangean function represent?

<p>The utility function adjusted for constraints. (A)</p> Signup and view all the answers

What can be derived from the condition that MRS_X,Y equals the relative price ratio?

<p>The consumer has reached optimal consumption of goods X and Y. (C)</p> Signup and view all the answers

Which inequality represents the condition applicable at consumer equilibrium?

<p>MU_X/PX = MU_Y/PY (A)</p> Signup and view all the answers

What is the implication of cross-multiplying in the equation MU_X/MU_Y = PX/PY?

<p>It shows the relationship between marginal utilities and prices. (D)</p> Signup and view all the answers

Which statement best describes the consumer's utility function U(F, C) = FC?

<p>Utility is derived from a multiplicative relationship between both goods. (A)</p> Signup and view all the answers

What is the relationship between the elasticity of demand for Good X and income $I$?

<p>It is equal to 1. (C)</p> Signup and view all the answers

In a Cobb-Douglas utility function, what does the equation $U(x,y) = x^{eta}y^{eta}$ imply about the consumer's preferences?

<p>The consumer allocates income proportional to the values of α and β. (A)</p> Signup and view all the answers

What does the budget constraint $I = p_x x + p_y y$ represent in the context of consumer choices?

<p>The total expenditure on goods x and y. (B)</p> Signup and view all the answers

How would you express the optimal choice of good X in terms of income and prices according to the given context?

<p>X* = (αI)/P_x (D)</p> Signup and view all the answers

If the sum of α and β in a Cobb-Douglas function equals 1, how does this affect the consumer's allocation of income?

<p>The consumer will allocate a constant percentage of income to each good. (C)</p> Signup and view all the answers

In the first-order conditions for a maximum, what do the equations $\frac{\partial \mathcal{L}}{\partial x} = 0$ and $\frac{\partial \mathcal{L}}{\partial y} = 0$ signify?

<p>The marginal utility per dollar spent on each good is equal. (C)</p> Signup and view all the answers

What does the equation $p_y y = \frac{(1-α)}{α} p_x x$ inform about the consumption choice between goods x and y?

<p>It establishes a fixed relationship between the amounts of good x and good y consumed. (C)</p> Signup and view all the answers

If a consumer's preferences are represented by the Cobb-Douglas utility function and α + β < 1, what is the effect on their consumption choices?

<p>They will spend less than their total income. (B)</p> Signup and view all the answers

Flashcards

Constrained Optimization

A problem where you aim to maximize or minimize an objective function while being bound by restrictions called constraints.

Objective Function

The function you want to maximize or minimize in a constrained optimization problem. It represents your goal.

Constraint

A limitation or restriction that must be satisfied in a constrained optimization problem.

Marginal Impact

The change in the dependent variable (like total cost) when you add one unit of the independent variable (like output).

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Equilibrium

A state in a system where things remain stable and unchanged as long as external factors don't interfere.

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Comparative Statics

Analyzing how changes in exogenous variables (outside factors) affect endogenous variables (outcomes) in a model.

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Reservation Price

The price at which someone is indifferent between doing something or not doing it. It's the price they are willing to pay or accept.

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Allocative Efficiency

The optimal allocation of scarce resources in a way that maximizes social welfare.

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Price Elasticity of Demand

Measures the responsiveness of quantity demanded to changes in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

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Elastic Demand

When the absolute value of price elasticity of demand is greater than 1. A change in price leads to a proportionally larger change in quantity demanded.

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Inelastic Demand

When the absolute value of price elasticity of demand is less than 1. A change in price leads to a proportionally smaller change in quantity demanded.

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Unit Elastic Demand

When the absolute value of price elasticity of demand is equal to 1. A change in price leads to an equal proportional change in quantity demanded.

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Total Revenue

The total income a company receives from selling its goods or services. Total revenue is calculated by multiplying price by quantity.

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Relationship between Elasticity and Total Revenue

When demand is elastic, a price increase leads to a decrease in total revenue. When demand is inelastic, a price increase leads to an increase in total revenue.

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Calculating Price Elasticity from Logarithmic Form

When a demand function is in logarithmic form, the coefficient of the price variable directly represents the price elasticity of demand.

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Interpreting Price Elasticity Values

A price elasticity of demand of -1.14 means that a 1% increase in price will cause a 1.14% decrease in quantity demanded.

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Budget Constraint

A graphical representation of all possible combinations of two goods that a consumer can afford to buy, given their income and the prices of the goods.

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Income (I)

The total amount of money a consumer has available to spend on goods and services.

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Price of X (PX)

The cost of one unit of good X.

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Price of Y (PY)

The cost of one unit of good Y.

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Relative Price

The price of one good in terms of another good. It's the amount of one good that must be given up to obtain one unit of another.

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Slope of the Budget Constraint

The negative of the relative price of X. It represents the rate at which a consumer can trade good X for good Y.

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Changes in the Budget Constraint

A shift in the budget line that occurs when there is a change in income, the price of X, or the price of Y.

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Consumer Equilibrium

The point where a consumer maximizes their utility (satisfaction) given their budget constraint.

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Marginal Utility of X

The additional satisfaction a consumer gains from consuming one more unit of good X, holding the consumption of all other goods constant.

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Marginal Utility of Y

The additional satisfaction a consumer gains from consuming one more unit of good Y, holding the consumption of all other goods constant.

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Marginal Rate of Substitution (MRSx,y)

The rate at which a consumer is willing to give up good Y to obtain one more unit of good X, while maintaining the same level of utility.

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Diminishing MRS

The MRS decreases as the consumer consumes more of good X and less of good Y, meaning they are willing to give up less and less of Y for each additional unit of X.

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Perfect Substitutes

Two goods that provide the same level of satisfaction to the consumer, regardless of the ratio in which they are consumed.

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Linear Utility Function

A utility function where the marginal utility of each good is constant and the goods are perfect substitutes.

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Constant MRS

The MRS remains the same as the consumer substitutes X for Y along an indifference curve.

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Increasing Marginal Utility

The marginal utility of a good increases as the consumer consumes more of it.

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Demand Elasticity

Measures how much the quantity demanded of a good changes in response to a change in price or income.

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Income Elasticity

Measures how much the quantity demanded of a good changes in response to a change in income.

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Cross-Price Elasticity

Measures how much the quantity demanded of one good changes in response to a change in the price of another good.

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Cobb-Douglas Utility Function

A mathematical function representing consumer preferences where the consumer's utility (satisfaction) depends on the consumption of two goods, with diminishing marginal utility for each good.

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Lagrangian Multiplier

A tool used in constrained optimization to find the maximum or minimum value of an objective function subject to one or more constraints.

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First-Order Conditions

Mathematical expressions that indicate where the maximum or minimum value of a function occurs, often derived by setting the derivative of the function to zero.

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Consumer's Choice

The combination of goods a consumer chooses to purchase given their budget constraint and preferences.

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Optimal Allocation

How a consumer divides their income between different goods to maximize their utility.

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MRS = Price Ratio

At consumer equilibrium, the marginal rate of substitution (MRS) between two goods equals the ratio of their prices. This means the consumer is willing to trade goods at the same rate as the market.

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Utility Maximization

Consumers aim to maximize their total utility, which is the satisfaction they get from consuming goods and services. They make choices to reach the highest possible utility level.

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Marginal Utility

The additional satisfaction a consumer gets from consuming one more unit of a good. It usually diminishes as you consume more of that good.

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Lagrangean Function

A mathematical tool used to find the maximum or minimum value of a function (utility) subject to constraints (budget).

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Study Notes

General Economics Study Notes

  • Economics is the study of how society allocates its scarce (limited) resources to satisfy unlimited wants.
  • Choices are made by considering the expected benefits and costs of decisions, and their consequences.
  • Microeconomics studies the economic behavior of individual decision-makers (consumers, firms, etc.) and markets.
  • Macroeconomics examines the overall economy and its aggregates (like GDP, inflation, unemployment).

Model Building in Economics

  • Models simplify complex real-world situations.
  • Exogenous variables are taken as given outside the model.
  • Endogenous variables are determined within the model.

Constrained Optimization Models

  • Economists use constrained optimization to model situations where decision-makers want to choose the best outcome given limitations or constraints.
  • In mathematical terms, the relationship to be optimized is call the objective function, and the limitations or conditions the constrains to the problem.

Equilibrium Analysis

  • Equilibrium analysis examines states or conditions that will persist until an outside factor causes change.
  • Markets move towards equilibrium where quantity demanded equals quantity supplied and price is in balance

Comparative Statics

  • Comparative Statics can be used to calculate how one variable will affect another following a change in an exogenous variable

Cost-Benefit Approach

  • If the benefit of an activity exceeds its cost, do it.
  • Reservation Price is the price at which a person is indifferent between doing an activity and not doing it.
  • Market prices are often determined by the tension between buyers' desire for lower prices and sellers' desire for higher prices.

Positive and Normative Economics

  • Positive economics describes how the economy actually works.
  • Normative economics offers recommendations about how the economy should operate.

Ceteris Paribus Assumption

  • All other relevant factors are constant, while analyzing the effects of one factor

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Intermediate Microeconomics Theory PDF

Description

This quiz covers essential concepts of microeconomics including budget lines, elasticity, and consumer demand. It explores how changes in income and prices affect purchasing decisions and total revenue. Test your knowledge on the implications of these variables in economic theory.

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