Question 1

An example of constrained optimization would be
A) a firm trying to maximize its profits subject to its budget constraint.
B) a ball coming to rest at the bottom of a cup.
C) an analysis of how market prices change when supply conditions change.
D) An analysis of the effect of facilitating internet trading on market price.

Accepted Answer

Constrained optimization involves optimizing a certain objective while also considering certain constraints that must be satisfied. In this case, a firm is trying to maximize its profits, but is constrained by its budget. Therefore, it is an example of constrained optimization. The other options do not involve constraints.

Question 2

A manager cares about the number of workers under her command. She can choose between two projects: Project A allows her to hire workers who must be paid W_A each, Project B allows her to hire workers who must be paid W_B each. She is allocated a budget of $100 that she can allocate to either project. Which of the following accurately represents the manager's problem? A) The objective function is Max (N_A+N_B), where N_i is the number of workers on project i (i = A, B); the constraint is W_AN_A + W_BN_B ≤ $100, where W_i is the wage on project i (i = A, B). B) The objective function is Max (N), where N is the number of workers under the manager's control; the constraint is W_A + W_B ≤ $100, where W_i is the wage on project i (i = A, B). C) The objective function is Max (W_AN + W_BN), where N is the number of workers and W_i is the wage of the worker on project i (i = A, B); the constraint is W_A + W_B ≤ $100. D) Max (B/N), where B is the manager's budget and N is the number of workers under the manager's command; the constraint is W_AN + W_BN ≤ $100.

Accepted Answer

The objective function should be to maximize the total number of workers on both projects, which is represented by N_A + N_B. The constraint should be that the total cost of hiring workers should not exceed $100, which is represented by W_AN_A + W_BN_B ≤ $100. Option A accurately represents this problem. Option B only considers the budget constraint and does not take into account the objective of maximizing the number of workers. Option C has the correct objective function but does not have the correct constraint. Option D does not have the correct objective function and does not consider the number of workers on each project.

Question 3

The three tools used repeatedly in microeconomic analysis are:
A) unconstrained optimization, comparative equilibrium, equilibrium statics.
B) opportunity cost, scarce resources, shifting equilibrium.
C) restricted analysis, constrained equilibrium, optimization.
D) constrained optimization, equilibrium analysis, comparative statics.

Accepted Answer

The three tools used repeatedly in microeconomic analysis are constrained optimization, equilibrium analysis, and comparative statics. Constrained optimization involves finding the optimal solution given certain constraints. Equilibrium analysis involves analyzing the interactions between buyers and sellers and determining the market-clearing price and quantity. Comparative statics involves studying the effects of changes in exogenous variables on endogenous variables, assuming the system is in equilibrium.

Question 4

Suppose a consumer's level of satisfaction is given by AB² and he/she has a total of $10 to spend on goods A and B. If the price of A is $1 and the price of B is $2, and assuming you can only purchase whole units (not fractional) of A and B, how many units of A and B should he/she purchase? A) 2 units of A and 4 units of B. B) 4 units of A and 3 units of B. C) 6 units of A and 2 units of B. D) 0 units of A and 5 units of B.

Accepted Answer

To maximize the consumer's satisfaction, we need to allocate the budget between goods A and B in such a way that the marginal utility per dollar spent on each good is equal.

The marginal utility of A is given by the first derivative of the utility function with respect to A, which is ABS1U1P1. Plugging in the prices, we get ABS1U11 = 1.

Similarly, the marginal utility of B is ABS1U2P2S1P0, which evaluates to ABS1U21 = 0.5.

Therefore, the consumer should allocate the budget in a way that he/she gets the same marginal utility per dollar spent on each good. Since the marginal utility per dollar spent on A is higher than that of B, it makes sense to purchase more units of A than B.

Using the budget constraint, we can set up the following optimization problem:

Maximize ABS1U1P12S1S1P0 
Subject to: P1A + P2B = 10

Plugging in the prices, the problem becomes:

Maximize ABS1U11A2S1S1P0 
Subject to: A + 2B = 10

Using trial and error, we can find that the optimal allocation is 4 units of A and 3 units of B, which gives a total utility of ABS1U14S1S1P0 = 26.

Question 5

Economics is often described as
A) The science of choice
B) The science of constrained choice
C) The science of supply and demand
D) The science of market forces

Accepted Answer

Economics is the science of constrained choice because individuals and societies have unlimited wants and needs but limited resources. As a result, they must make choices about how to allocate those resources, taking into account opportunity costs and trade-offs.

Question 6

Which of the following statements regarding exogenous and endogenous variables is correct?
A) The set of exogenous variables in any economic model should take into account the rich detail of the world and so should be limitless.
B) Endogenous variables will always be determined within the model.
C) Exogenous variables change as a result of changes in endogenous variables.
D) The only variables that are relevant to the market equilibrium are the endogenous variables, as they are determined within the model.

Accepted Answer

Endogenous variables are those that are determined within the model, while exogenous variables are considered outside the model and are often determined by factors outside of the model. Therefore, option B is the correct statement about endogenous variables. Option A is false because including too many exogenous variables can create a problem of overfitting, resulting in a less accurate model. Option C is incorrect because changes in exogenous variables can affect endogenous variables, but it is the reverse of what is stated in the statement. Option D is incorrect because both endogenous and exogenous variables are relevant in determining market equilibrium.

Question 7

The analytical tools underlying nearly all microeconomic studies are:
A) Unconstrained optimization and comparative statics.
B) Comparative statics and game theory.
C) Opportunity cost and equilibrium analysis.
D) Constrained optimization, equilibrium analysis, and comparative statics.

Accepted Answer

Constrained optimization, equilibrium analysis, and comparative statics are the three analytical tools that underlie nearly all microeconomic studies. Constrained optimization involves finding the best solution to a problem subject to certain constraints. Equilibrium analysis involves analyzing the behavior of agents in a market or economy where supply and demand are in balance. Comparative statics involves comparing the behavior of agents in response to changes in exogenous variables. These three tools are essential for analyzing microeconomic phenomena such as market outcomes, consumer behavior, producer behavior, and market failures.

Question 8

Which of the following is the best example of a consumer's objective function?
A) profits.
B) consumption.
C) satisfaction
D) budget constraint.

Accepted Answer

A consumer's objective function is their ultimate goal, usually stated as maximizing utility or satisfaction from consumption. Therefore, "satisfaction" is the best example of a consumer's objective function. Choices A, B, and D are all factors that can influence a consumer's decisions, but they are not the ultimate objective.

Question 9

Which of the following is not typically found in a constrained optimization problem?
A) Resource constraint
B) Endogenous variable
C) Comparative statics analysis
D) Objective function

Accepted Answer

Comparative statics analysis is not typically found in a constrained optimization problem as it is related to analyzing the effects of changes in exogenous variables on the endogenous variables, whereas constrained optimization problems typically only focus on optimizing the endogenous variables subject to constraints. Resource constraints, endogenous variables, and objective functions are all essential components of constrained optimization problems.

Question 10

Constrained optimization, equilibrium analysis and comparative statistics are the three essential tools of
A) Macroeconomic analysis
B) Microeconomic analysis
C) Equilibrium analysis
D) Industry analysis

Accepted Answer

Constrained optimization, equilibrium analysis and comparative statistics are the three essential tools of microeconomic analysis. These tools are used to analyze how individual consumers and firms make decisions in the market and how these decisions lead to market outcomes. Macroeconomic analysis is concerned with the overall performance of the economy, while industry analysis focuses on specific industries. Equilibrium analysis is a concept used in both microeconomic and macroeconomic analysis, but it is not a tool on its own.

Question 11

Microeconomics examines
A) the economic behavior of an entire nation.
B) the economic behavior of individual economic decision units.
C) topics such as national income and inflation.
D) monetary policy.

Accepted Answer

Microeconomics is the study of how individuals and firms make economic decisions, how they interact in markets, and how governments can influence their behavior through public policies. It focuses on analyzing the behavior of individual decision units such as consumers, firms, and households. Therefore, option B is the correct answer as it talks about the economic behavior of individual economic decision units.

Question 12

Which of the following is an example of a constraint?
A) L+W
B) Max LW
C) $\text { min } A B$
D) L + W ? 5

Accepted Answer

A constraint is a limitation or restriction that needs to be taken into account in order to solve a problem. Choice D represents a constraint as it places a minimum value on the sum of L and W in the problem. Choices A and B are mathematical expressions that could represent constraints, but without further context it is not clear if they are being used as such in the problem. Choice C represents the minimum of two variables and is not a constraint.

Question 13

Suppose the price of $A$ is $3, the price of $B$ is $5, the consumer's income is $30, and the consumer's level of satisfaction is measured by $A + B$ . The consumer's income constraint is
A) $\max 3 A + 5 B$
B) $\max A + B$
C) $A + B \leq 30$
D) $3 A + 5 B \leq 30$

Accepted Answer

The consumer's income constraint is the maximum amount of money they can spend on $A$ and $B$ combined, which is their income of $30. Using the prices for $A$ and $B$, we get the inequality $3A + 5B \leq 30$ as the income constraint. The consumer's goal is to maximize their level of satisfaction, which is measured by $A + B$. Therefore, the consumer should choose the combination of $A$ and $B$ that satisfies the income constraint and maximizes $A + B$. Solving the inequality, we get the feasible region as $\{(0,0),(0,6),(3,3),(6,0)\}$. Among these choices, the combination that maximizes $A + B$ is $(6,0)$, which gives a level of satisfaction of 6.

Question 14

Identifying the appropriate way to allocate an economy's resources is an example of
A) a constrained optimization problem.
B) a comparative statics problem.
C) an equilibrium analysis.
D) marginal analysis.

Accepted Answer

Identifying the appropriate way to allocate an economy's resources involves optimizing the allocation, subject to various constraints such as limited resources and competing demands. This is an example of a constrained optimization problem. Comparative statics problems involve analyzing changes in an economic model, equilibrium analysis involves studying supply and demand interactions, and marginal analysis involves examining the additional benefits or costs of producing or consuming one additional unit of a particular good or service.

Question 15

Constrained optimization occurs when:
A) An individual makes choices that are influenced by his/her parents and family.
B) An individual makes choices that best suit his/her preferences.
C) Firms choose the best products to meet their client's needs.
D) An individual is forced to choose between competing alternatives subject to some limitation such as budgetary considerations.

Accepted Answer

Constrained optimization occurs when an individual is forced to choose between competing alternatives subject to some limitation such as budgetary considerations. Therefore, the correct choice is D.

Question 16

Every society must answer
A) Which variables are exogenous and which are endogenous?
B) Who will receive the goods and services?
C) What goods and services will be produced, how much will be produced, who will produce them and who will receive them?
D) How centralized should government bureaucracy be?

Accepted Answer

The question is asking about the fundamental question that every society must answer. The most fundamental of those questions is about the production and distribution of goods and services. Therefore, the answer is C which includes all the aspects related to this topic. The other options are not universal questions that every society must answer.

Question 17

The definition of an exogenous variable is
A) a variable whose value is determined within the model under study.
B) a variable whose value is determined outside the model under study.
C) a variable whose value is determined through constrained optimization.
D) a variable whose value is determined through comparative statics.

Accepted Answer

An exogenous variable is one whose value is determined outside of the model under study. It is not influenced by the other variables in the model, but it can impact the endogenous variables.

Question 18

In general, economics is the study of
A) the allocation of scarce wants to unlimited resources.
B) the allocation scarce resources to unlimited wants.
C) the allocation of resources between the government and the private sector.
D) the allocation of workers between firms.

Accepted Answer

Economics is the study of how societies allocate scarce resources to unlimited wants. This includes the production, distribution, and consumption of goods and services. The central problem of economics is how to allocate these scarce resources efficiently to satisfy the unlimited wants of individuals and society as a whole. Choice A is similar but has the allocation in reverse order. Choice C is too narrow and only focuses on the allocation of resources between two specific sectors. Choice D is also too narrow and only focuses on the allocation of workers between firms.

Question 19

An exogenous variable in a consumer's choice problem would typically be:
A) satisfaction level.
B) consumption level.
C) price level.
D) quantity consumed.

Accepted Answer

An exogenous variable is a variable that is outside of the control of the consumer and affects their decision-making process. Price level is an example of an exogenous variable, as the consumer cannot control the price of a good or service. Satisfaction level, consumption level, and quantity consumed are all endogenous variables, meaning they are directly influenced by the consumer's choices and preferences.

Question 20

An endogenous variable is
A) a variable that an economic agent chooses.
B) consumption, investment or government spending.
C) a variable determined within the economic system being studied.
D) a variable pertaining to the home country economy.

Accepted Answer

An endogenous variable is a variable determined within the economic system being studied. It is not necessarily limited to consumption, investment or government spending, and it is not limited to the home country economy. Option A is referring to a decision variable, not an endogenous variable. Option B gives examples of economic variables, but only one of them is endogenous. Option D is too limited in its scope.

Quiz 1: Analyzing Economic Problems

An example of constrained optimization would be

The three tools used repeatedly in microeconomic analysis are:

Suppose a consumer's level of satisfaction is given by AB2 and he/she has a total of $10 to spend on goods A and B. If the price of A is $1 and the price of B is $2, and assuming you can only purchase whole units (not fractional) of A and B, how many units of A and B should he/she purchase?

Economics is often described as

Which of the following statements regarding exogenous and endogenous variables is correct?

The analytical tools underlying nearly all microeconomic studies are:

Which of the following is the best example of a consumer's objective function?

Which of the following is not typically found in a constrained optimization problem?

Constrained optimization, equilibrium analysis and comparative statistics are the three essential tools of

Microeconomics examines

Which of the following is an example of a constraint?

Suppose the price of AAA is $3, the price of BBB is $5, the consumer's income is $30, and the consumer's level of satisfaction is measured by A+BA + BA+B . The consumer's income constraint is

Identifying the appropriate way to allocate an economy's resources is an example of

Constrained optimization occurs when:

Every society must answer

The definition of an exogenous variable is

In general, economics is the study of

An exogenous variable in a consumer's choice problem would typically be:

An endogenous variable is

Suppose a consumer's level of satisfaction is given by AB² and he/she has a total of $10 to spend on goods A and B. If the price of A is $1 and the price of B is $2, and assuming you can only purchase whole units (not fractional) of A and B, how many units of A and B should he/she purchase?

Suppose the price of $A$ is $3, the price of $B$ is $5, the consumer's income is $30, and the consumer's level of satisfaction is measured by $A + B$ . The consumer's income constraint is