chapter 1
In the consumption function C = $1000 + .3Y, C is consumption and Y is national income. How much is consumption when national income is zero?
$1000 Explanation: The constant term, $1000, is the amount of consumption that consumers have when they have no income. They are spending out of their savings.
Suppose a line shows that every time a family's income increases by $1, the family's spending increases by $0.90. If income increased by $300, the spending must have increased by
$270. Explanation: If the change in spending is 90% of the change in income, and if income rises to $ 300, spending would rise to $270.00 (.9 times 300).
Given the demand formula for frisbees P = $8.30 − 1.23Q, what is the proper interpretation of the value of $8.30?
$8.30 represents the price that would cause the quantity of frisbees demanded to fall to zero. Explanation: When frisbee purchases drop to zero (i.e., Q = 0), the price that would motivate the drop in frisbee purchases would be $8.30: (P = $8.30 - 1.23(0) = $8.30).
Given a demand formula for frisbees of P = $8.30 − 1.23Q, what is the proper interpretation of the value of −1.23?
-1.23 represents the decrease in price necessary to cause the quantity demanded of frisbees to increase by one unit. Explanation: A negative slope value (-1.23) suggests that a negative relationship exists between the two variables.
Consider the equation of linear function y = −4 + 7x. If it were graphed, the intercept would be
-4. Explanation: The intercept of function is the constant term. In this example, the constant term is -4 or the value of y when x is 0.
According to the graph, the society has to give up _______ pounds of food to build one car.
1/10
Suppose Canada produces only beer and oil. One unit of labor can produce, in a one hour period, either 100 barrels of beer or 10 barrels of oil. Examine the PPF for Canada. What is Canada's opportunity cost for one barrel of beer?
1/10 of a barrel of oil Explanation: Use the endpoints on the PPF. Set up a ratio of oil to beer: 10/100 = 1/10 barrel of oil.
According to the graph, the society has to give up _______ cars to produce another pound of food.
10 Explanation: On the linear PPF, the opportunity cost of food in terms of cars is found by dividing the endpoints, 1000/100 = 10. The society gives up 10 cars to produce another pound of food. The good for which you want the cost is in the denominator.
Suppose Canada produces only beer and oil. One unit of labor can produce, in a one hour period, either 100 barrels of beer or 10 barrels of oil. Examine the PPF for Canada. What is Canada's opportunity cost for one barrel of oil?
10 barrels of beer Explanation: Using the endpoints of the PPF, set up a ratio of beer to oil: 100/10 = 10 barrels of beer.
Given the equation for a linear function, 20 + .67x = y, what is the value of y when x is zero?
20 Explanation: The value of the variable y, when the variable x is zero, is equal to the constant term. In this equation the constant is 20.
Consider the equation of linear function y = −4 + 7x. If it were graphed, the slope would be
7. Explanation: The slope of the function is the change in y as the variable x changes.
The slope of the line is defined by
A and C. Explanation: The slope is determined by the change in y over the change in x and is used to figure the demand formula.
Which of the following examples represents a method of presenting data in terms of the relative size of vertical columns?
A bar graph
The slope of a line on a graph is defined as
B and C. Explanation: The slope of a line on a graph is calculated by dividing the change in the y-axis variable by the change in the x-axis variable. The common expression is "rise over run."
Which point on the graph is not attainable?
C Explanation: Point C is outside the curve, meaning that it falls outside of the possibilities for this society. Any point beyond the curve means that this society does not have the resources or technology to produce the combination.
From the graphs below, who has a comparative advantage in mopping, Nick or Carl?
Carl Explanation: Examine the slope of the PPFs for Carl and Nick. Carl's PPF is flatter than Nick's; therefore Carl has a comparative advantage in the good on the horizontal axis: mopping.
Russia can produce a bushel of corn with four workers and a bushel of rice with three workers. China can produce a bushel of corn with three workers and a bushel of rice with two workers. Which country has an absolute advantage for either good?
China has an absolute advantage for both goods. Explanation: An absolute advantage indicates that you can make more with less resources than others. In this case, China can produce more corn and rice with fewer workers than Russia.
Russia can produce a bushel of corn with four workers and a bushel of rice with three workers. China can produce a bushel of corn with three workers and a bushel of rice with two workers. How would these countries specialize?
China would specialize in producing rice, and Russia would specialize in producing corn. Explanation: China's opportunity cost for corn is one and one-half bushels of rice. Russia's opportunity cost for corn is one and one-third bushels of rice. Each country's opportunity cost of the other good is the reciprocal of the first one. Therefore, China should specialize in rice and Russia should specialize in corn. Each specializes in the product for which it has a comparative advantage.
Which of the following resources is scarce?
Clean air Explanation: Scarcity is the imbalance between what is freely available and what people want. Clean air has a cost so it is not freely available.
When the demand curve shifts, the intercept remains the same.
False Explanation: A shift in a demand curve means that an outside variable has changed. The entire demand curve, including the intercept, shifts parallel to itself.
If a country's PPF shows capital goods on one axis and consumer goods on the other axis, the country's PPF will shift out faster if it spends more on consumer goods in the current time period
False Explanation: The country's PPF will shift out faster if the country invests in capital goods and foregoes current consumption. Capital goods represent an investment in future productive capacity.
The slope of a demand curve is the change in the x-axis divided by the change in the y-axis.
False Explanation: The slope is the change in the y-axis divided by the change in the x-axis. It is the "rise over the run."
Which of the following is not a scarce good?
Garbage Explanation: Garbage is not a scarce resource because no one wants garbage. In fact, most people pay to have it removed. Air, space, and water are commodities because, under certain circumstances, people will pay for them.
Russia can produce a bushel of corn with four workers and a bushel of rice with three workers. China can produce a bushel of corn with three workers and a bushel of rice with two workers. Which country has a comparative advantage in the production of corn and which has a comparative advantage in rice?
Russia has a comparative advantage in the production of corn, and China has a comparative advantage for the production of rice. Explanation: Comparative advantage indicates that one country can produce one good more efficiently than the other. In this case, Russia has a lower opportunity cost for producing corn, and China has a lower opportunity cost for producing rice. Russia's opportunity cost for corn is 4/3, or 1.33 bushels of rice; China's opportunity cost for corn is 3/2, or 1.5 bushels of rice. Russia's opportunity cost for rice is 3/4, or 0.75 bushels of corn; China's opportunity cost for rice is 2/3, or 0.67 bushels of corn.
An inward shift in the production possibilities frontier (PPF) could be the result of a decline in the general level of education.
True Explanation: A decline in education will be reflected in declines in technological advances, worker productivity, etc. Such declines will result in a decrease in production possibilities (an inward shift of the PPF).
A relatively flat demand curve indicates that the demand for a product is very sensitive to a change in price.
True Explanation: A flat demand curve indicates that a small change in price will cause a large change in quantity demanded.
Mandatory retirement at age 55 will cause an inward shift in the PPF.
True Explanation: A mandatory early retirement age would make less labor resources available for production purposes. Accordingly, the reduction in labor resources would cause the PPF to shift inward.
The slope of a linear function depends on the units of measurement.
True Explanation: Slope changes if you use different units of measurement. For example, changing the price on a demand curve from dollars to cents changes the slope.
When a demand curve shifts, the slope of the curve remains the same.
True Explanation: The demand curve shifts parallel to itself. The slope does not change. The intercept, however, does change.
In an economy, assume that labor is the only factor of production. One worker can produce either twelve pounds of food a year or six rifles. The slope of the country's PPF is −2 if rifles are on the horizontal axis.
True Explanation: The opportunity cost of rifles in terms of food is two pounds of food. Set up a fraction with the good whose cost you want as the denominator and the one you have to give up as the numerator. In this example, the fraction is 12/6 = 2. Even though it technically is negative, use the absolute value as the cost. The slope is the opportunity cost of the good on the horizontal axis.
The vertical intercept is defined in the demand formula as the constant number.
True Explanation: The vertical intercept is the price value where no quantity is demanded and is represented as $12 in the demand formula P = $12-.50Q.
Given the equation for a linear function, a + bx = y, which term represents the intercept?
a Explanation: The intercept term is a constant. In the general formula for a linear function, a is a constant and is the intercept of the line.
A shift in the production possibilities frontier curve will occur as a result of all of the following except
a change in the production of one good relative to another good. Explanation: An outward shift of the PPF curve occurs when technology increases, new resources are discovered, population increases, or capital increases. All of these factors are increases in societal endowments and will extend the PPF. A change in the production of one good relative to another good simply changes the combination being produced and does not represent a change in possibilities. This change is movement along the PPF curve.
Fitting a line with a positive slope to a scatter diagram indicates
a direct relationship of the variables
Examine the accompanying graph of a PPF for an agricultural society. The most likely cause of the shift of the PPF is
a drought in wheat-producing states. Explanation: Decreased wheat production with every possible level of rice production causes a skewed PPF. The shift is a rotation from one axis.
A choice to produce more of one good and less of another results in
a movement along the PPF curve. Explanation: An increase in the production of one good and a decrease in another represents a new combination on the existing production possibilities curve.
The total product curve
all of the above. Explanation: The total product curve is the graph of the production function. It is not linear and changes slope over the range of output.
The production possibilities frontier illustrates the supply side of an economy because
both A and B. Explanation: The PPF shows supply because it gives possible combinations of what to produce without taking into consideration consumer preferences. The PPF presents a range of possibilities from which society must choose.
Rational choice
both a and c. Explanation: Rational choice requires the undertaking of costs-benefit analysis (i.e., the determination of the "best" choice) to ultimately maximize self-interest.
A country that has an absolute advantage in a good
can produce the good using fewer resources than its trading partner. Explanation: An absolute advantage means that a country can produce a good with fewer resources, that is, at a lower absolute cost than the trading partner. However, the country should specialize in the goods for which it has a comparative advantage. Absolute advantage is not part of the decision to specialize and trade.
On a demand curve, an increase in the price of a good will
cause a decrease in the quantity demanded. Explanation: An increase in the price of a good causes the quantity demanded to fall. This decrease in quantity demanded is represented by movment along the demand curve. A change in any variable, except price, causes the demand curve to shift and is called a change in demand.
Each point on a two-dimensional graph consists of
combinations of variables that represent two pieces of information. Explanation: Each point contains information that represents the variables that are on each axis.
Two producers can gain from trade if the trade is based on
comparative advantage. Explanation: The basis of trade is comparative advantage, or lower opportunity costs. Two trading partners can both gain if they trade based on their comparative advantages.
For country A to have a comparative advantage in the production of agricultural products means that, relative to country B, with the same resources,
country A is better at producing agricultural products than country B. Explanation: Comparative advantage is a relative measure. If a country is better at producing something relative to another country, then it has a comparative advantage.
Examine the accompanying graph of a society's PPF. The most likely cause of the shift from PPF1 to PPF2 is
destruction of resources because of a war. Explanation: Destruction of resources means that the society cannot produce as much of either category of goods as before. The PPF shifts inward.
If one variable increases when another one increases, then we say that the two variables are
directly related. Explanation: Variables are directly related when both change in the same direction. This phenomenon is also known as a positive relationship.
When a production possibilities frontier shifts outward, society experiences
economic growth. Explanation: When the PPF shifts outward, the economy is able to produce more of all goods. This change is the definition of economic growth. The PPF does not address the questions of allocation or income distribution.
Economic scarcity
exists in all economies.
When each trading partner specializes in the production of a good for which it has a comparative advantage, each partner can gain from trade, but total production remains unchanged.
false Explanation: By specializing in those goods for which it has a comparative advantage, each partner can produce the goods that it produces best and can allow others to produce those goods that they produce best. The result is that total production can increase over non-specialized production.
In any trade between two trading partners and two goods, it is possible for one of the partners to have a comparative advantage in both goods.
false Explanation: Comparative advantage is caused by differences in opportunity costs, not resource endowments. In the two-person, two-good model, a trading partner who has a comparative advantage in one good by definition has a comparative disadvantage in the other good.
Economists only use three-dimensional graphs when using three variables.
false Explanation: Economists can use two-dimensional graphs to map three variables. Each axis represents a variable; additional variables can be represented as isoquants.
In the production possibilities frontier, points A, B, and C represent feasible outcomes for this society.
false Explanation: Points A and B are feasible and efficient combinations, because they lie on the production possibilities curve. Point C, however, is outside the realm of possibilities; therefore, it is unattainable
If trade benefits one country, it will make the other country worse off.
false Explanation: With specialization, trade makes both countries better off. Each country gets a wider variety of goods to consume and total output increases.
Bobby can vacuum two rooms in ten minutes or dust two rooms in twenty minutes. Bobby's schedule of possibilities indicates that
he can dust three rooms and vacuum six rooms in one hour.
Economics is the study of
how to manage society's scarce resources. Explanation: Given the fact that all societies face limited resources, the economic problem that they face is how to manage those resources to the greatest benefit.
A good is not scarce
if everybody can have all they want of it. Explanation: Scarcity means an imbalance between what people want and what is freely available. If a good is freely available it is called a "free good" and is not scarce.
If two variables, consumption (C) and income (I), are directly related we can say that
if income increases, then consumption increases.
The idea of opportunity costs indicates that
if the production of one good is increased, the production of another good must decrease
If everyone made rational choices,
individuals would still differ in their choices. Explanation: Individuals make different choices because they have different information and different constraints. Economists assume that individuals act rationally given their constraints and information.
A scatter plot is
information arrayed in a two-dimensional space to represent two variables for each data point.
Referring to the graph, if this economy moves from point A to point B,
it must give up military equipment to get more food. Explanation: The PPF curve represents the efficient production combinations of two goods. In this case, a movement from point A to point B represents the trade-off of production of more food and less military equipment.
When two people divide their labor according to their comparative advantages,
more work can be completed in a given period of time. Explanation: Dividing labor based on comparative advantage means that the two people can divide their labor based what each does best. When this division occurs, each specialized and more production can take place than if they did not trade their labor.
Russia can produce a bushel of corn with four workers and a bushel of rice with three workers. China can produce a bushel of corn with three workers and a bushel of rice with two workers. The opportunity cost for China to produce one bushel of corn is
one and a half bushels of rice. Explanation: The opportunity cost for China to produce one bushel of corn is measured in terms of the amount of rice given up. In this case, each Chinese worker can produce one-half bushel of rice. For China to produce an additional bushel of corn it has to move three workers from rice production to corn production and will lose one and one-half bushels of rice.
Russia can produce a bushel of corn with four workers and a bushel of rice with three workers. China can produce a bushel of corn with three workers and a bushel of rice with two workers. The opportunity cost for Russia to produce one bushel of corn is
one and one-third bushels of rice. Explanation: The opportunity cost for Russia to produce one bushel of corn is measured in terms of the amount of rice given up. In this case, one and one-third bushels of rice aregiven up. Each worker inRussia can produce one-third bushel of rice. To produce another bushel of corn Russia must move four workers from rice to corn production and lose one and one-third bushels of rice.
A negative relationship between variables exists when
one variable increases while the other variable decreases. Explanation: A negative relationship, also called an inverse relationship, describes a situation in which an increase in one variable causes a decrease in another variable. Negative relationships are graphed with a downward-sloping curve.
The display of three variables in a two-dimensional graph are organized with
one variable on each axis and the other variable held constant as the value on the isoquant.
Suppose a person can produce either two bushels of wheat per hour or six bushels of corn per hour. This person's opportunity cost of one bushel of corn is
one-third of a bushel of wheat. Explanation: To find the opportunity cost of one good in terms of another, you must determine how much of one good that you give up to get another. Divide the amount of the product you are giving up by the amount of the product whose cost you want. Be sure that the time resource used is the same for each good. In this problem, the opportunity cost of corn in terms of wheat is two bushels of wheat/ six bushels of corn or 1/3 bushel of wheat given up to produce another bushel of corn.
In a farming economy that produces barley and flax, a new fertilizer is invented. The fertilizer only works on barley. The production possibilities frontier will
only shift outward on the barley axis. Explanation: A fertilizer that only affects barley will cause the PPF to shift outward only on that axis. The technology for the other crop does not change; therefore, its axis remains the same.
The economic term "specialization" refers to the behavior of trading partners when each partner
produces only those goods for which it has a comparative advantage Explanation: Comparative advantage is defined by the relative, or lower, opportunity costs of one trading partner compared with another and should result in an improved production possibilites frontier.
Any combination of two goods lying outside the production possibilities frontier
represents an unattainable combination of goods.
Scarcity
requires people to make choices.
A decrease in a consumer's income causes his demand curve to
shift inward. Explanation: A decrease in income, an exogenous variable, causes an inward shift in demand. The consumer can afford to buy fewer of the goods at every price.
In a farming economy of wheat and rice, a warming trend occurs. This trend increases the production of both goods. However, the rice production is affected more than the wheat. The production possibilities frontier will
shift outward for both goods, but the rice axis will shift further. Explanation: The PPF will shift outward representing the increase in production for both goods. The axis for rice will shift more than the axis for wheat.
A shift in the demand curve
shifts the whole demand curve inward or outward. Explanation: A shift in the demand curve occurs when an exogenous variable either increases or decreases, causing the demand curve to shift to the right or to the left.
A steeply sloping demand curve shows
that the change in quantity demanded (x-axis) is not very sensitive to a change in price (y-axis). Explanation: The downward-sloping demand curve indicates an inverse relationship between price and quantity demanded. A steep slope indicates that quantity demanded is not very sensitive to a change in price.
The slope of a demand curve describes consumer behavior by showing
that the consumer increases his/her consumption of a good when the price goes down. Explanation: The demand curve slopes downward indicating that a consumer's quantity demanded increases as price decreases and decreases as price increases. The slope illustrates the law of demand.
A rational person makes a choice if
the benefits outweigh the costs. Explanation: A rational person chooses actions based on benefits being greater than costs.
Opportunity cost is defined as
the best alternative that you give up when you make a choice. Explanation: Because of scarcity, opportunity cost is a means by which to evaluate alternative choices. It is the best alternative that we give up when we make choice.
If you wait in line one hour to buy a concert ticket for $30, the opportunity cost of that ticket is
the best alternative to both the $30 and the one hour. Explanation: The opportunity cost of this trade is both the alternative use of the money and the time.
In this production possibilities frontier, if the consumer moves from A to B,
the consumer is choosing more leisure and less income. Explanation: The consumer has a trade-off between income and leisure. The more the consumer works, the more his income increases but the more leisure time he gives up. Time is the resource that is scarce.
An inward shift in the PPF could be caused by
the destruction of resources in a war. Explanation: The PPF would shift inward when resources are destroyed. A destruction of resources would cause production of all goods to fall and represents the opposite of growth.
Economic value is defined as
the difference between the benefits and costs of an activity. Explanation: The basic definition of economic value is the difference between the benefits and costs of an activity. Accordingly, profit (the excess of business revenues over business costs) represents the concept of economic value as applied to business operations.
The slope of a downward-sloping straight line is calculated as
the distance from the vertical intercept of the line to the origin divided by the distance from the origin to the horizontal intercept of the line.
In a two-person, two-good trading model, the individual with a flatter production possibilities frontier has a comparative advantage in
the good on the horizontal axis. Explanation: A relatively flat production possibilities frontier means that the individual gives up little of the good on the vertical axis to specialize in the good on the horizontal axis. In the model, the individual would specialize in the production of the good for which she has a comparative advantage, that is, a lower opportunity cost.
The opportunity cost of a college education is
the highest salary that you could make if you worked full-time instead of going to school. Explanation: The opportunity cost of any activity is the highest valued activity that you give up when you make a choice. In the case of a college education, the highest valued activity is usually the salary you could make if you were not going to school and were working instead. Opportunity cost is always something that is given up.
Each coordinate of a graph is written as
the horizontal axis x and the vertical axis y (x, y).
Scarcity is defined as
the imbalance between what is wanted and what is freely available. Explanation: By definition, scarcity is concerned with the imbalance between what is wanted and what is freely available. The mismatch between the goods and services wanted and the inputs needed to produce such goods and services is at the core of the study of economics.
The opportunity cost of attending college includes
the income you could have earned while in classes. Explanation: Potential income is something that one gives up to attend college.
The production possibilities frontier is a straight line when
the opportunity cost is constant. Explanation: The PPF is a straight line when all the resources of an economy are well suited for all uses. The PPF has a constant slope and a constant opportunity cost.
In weighing costs against benefits in any economic trade, the total cost can be viewed as
the opportunity cost. Explanation: The total costs of any economic trade can be considered the opportunity cost.
If there is an agricultural economy in which land can be used either as pasture for cattle or as crop land for wheat, the opportunity cost of converting one acre from pasture to wheat production is the
the pounds of beef that are lost. Explanation: The opportunity cost of turning the acre into wheat production is the lost beef production that results. Opportunity cost is always measured in terms what must be given up.
A graph of the demand curve measures
the relationship between the price of a product and the quantity demanded. Explanation: The demand curve shows the relationship between a product's price and the quantity demanded.
On an exponentially increasing curve,
the slope is not constant. Explanation: The slope of an exponentially increasing curve is not constant and changes from point to point on the curve. The curve is not linear.
The PPF is a tool in economics to illustrate
the study of rational choice in situations of scarcity.
Alternatively, economics may be defined as
the study of the creation and distribution of economic value. Explanation: Given the scarcity of resources, economics is very concerned as to whether the usage of resources is producing economic value.
Which of the following statements regarding the tangent line is false?
the tangent line cannot be used to find the slope of the TP curve. Explanation: The tangent line touches the TP curve and has a slope equal to the TP curve at the point it touches. A tangent line is always used to find the slope of the TP curve at any point.
The production possibilities frontier (PPF) represents
the various combinations of output that an economy can produce with its available resources and technology. Explanation: The PPF shows all the possible combinations on the curve that represent a maximum amount of one good produced for a certain quantity of another good produced. Points beyond the graph are impossible points; points inside the graph are inefficient points.
If the price of a soft drink changes from $1.00 to $2.00, then
there is a change in quantity demanded. Explanation: When there is a change in the price of a good, there is a change in quantity demanded. A change in quantity demanded is shown by movement along the demand curve. There is no change in demand which is a shift in the demand curve.
Economists prefer elasticities for all of the following reasons except that
they are based on total changes in units. Explanation: Elasticities are based on percent changes and illustrate a relationship that is independent of the type of unit. Elasticity is unaffected by the units of measurment.
Suppose a person can produce either two bushels of wheat per hour or six bushels of corn per hour. This person's opportunity cost of one bushel of wheat is
three bushels of corn. Explanation: To find the opportunity cost of one good in terms of another, you must determine how much of one good that you give up to get another. Divide the amount of the product you are giving up by the amount of the product whose cost you want. Be sure that the time resource used is the same for each good. In this problem, the opportunity cost of wheat in terms of corn is six bushels of corn/ two bushels of wheat or three bushels of corn given up to produce another bushel of wheat. The opportunity cost of one product is the reciprocal of the opportunity cost of the other product.
When increasing opportunity costs exist, resources are not perfectly substitutable for each other.
true Explanation: A concave production possibilities curve (PPF) reflects the trade-off of greater quantities of a good when more of the other good is produced. Accordingly, the greater trade-off reflects the incompatability of resources.
An example of an isoquant is a curve that shows the combinations of longitude and latitude that have the same altitude.
true Explanation: An isoquant is the name of the curve that shows the pairs of values for the variables (latitude and longitude) on two axes of a graph for which a third variable (altitude) has a given value. The third variable is constant and its value is the numerical value of the isoquant.
The slope of the production function is flatter near the bottom of the curve.
true Explanation: The production function defines the relationship between output and number of workers. When there are few workers, each worker is not very productive. Therefore, the curve is flat near the bottom.
Points on the production possibilities frontier are the only efficient production points.
true Explanation: The production possibilities frontier graphically illustrates all production combinations that are efficient. That is, the PPF curve shows which combinations efficiently use an economy's resources. Points outside the curve are unattainable, and points inside the curve are inefficient.
Bobby can vacuum two rooms in ten minutes or dust two rooms in twenty minutes. Using his unit labor requirement, Bobby's potential for vacuuming is
twelve rooms per hour or dusting is six rooms per hour. Explanation:
Bobby can vacuum two rooms in ten minutes or dust two rooms in twenty minutes. The opportunity cost of dusting one more room is
vacuuming two rooms. Explanation: The opportunity cost is giving something up in order to perform another activity. In this case, Bobby gives up vacuuming two rooms to dust one more room.
Suppose a PPF has capital goods on the vertical axis and consumption goods on the horizontal axis. The PPF has a constant slope with a vertical intercept of 80 and a horizontal intercept of 160. Last year, 160 units of consumption goods were produced, so the economy produced __________ units of capital goods.
zero Explanation: The PPF is the entire range of possibilities for the economy. When the economy maximizes its production of one good, it is unable to produce any of the other good. The intercepts on each axis represent the maximum for each good.
Bobby can vacuum two rooms in ten minutes or dust two rooms in twenty minutes. Assuming that dusting is on the vertical axis, the slope of Bobby's production possibilities frontier is
−1/2. Explanation: The slope is rise / run, or the change in y divided by the change in x. You can use the end points, twelve rooms dusted and six rooms vacuumed, to determine the slope. The slope is 6/12 = −1/2.
