How does opportunity cost vary

Now imagine a student, whom we will call Alexei. He can vary the number of hours he spends studying. We will assume that, as in the Florida study, the hours he spends studying over the semester will increase the percentage grade that he will receive at the end, ceteris paribus. This relationship between study time and final grade is represented in the table in Figure 3. In this model, study time refers to all of the time that Alexei spends learning, whether in class or individually, measured per day not per week, as for the Florida students.

The table shows how his grade will vary if he changes his study hours, if all other factors—his social life, for example—are held constant. You can think of the production function as telling us what Alexei will get under normal conditions if he is neither lucky nor unlucky. If we plot this relationship on a graph, we get the curve in Figure 3. Alexei can achieve a higher grade by studying more, so the curve slopes upward. Any time spent studying beyond that does not affect his exam result he will be so tired that studying more each day will not achieve anything , and the curve becomes flat.

If he works for 4 hours per day, he achieves a grade of Follow the steps in Figure 3. It shows how an input of study hours produces an output, the final grade. At 15 hours of study per day Alexei achieves his maximum possible grade, After that, further hours will make no difference to his result: the curve is flat.

Therefore, at 4 hours of study, the marginal product of an additional hour is 7. At 10 hours of study, the marginal product of an additional hour is 3. As we move along the curve, the slope of the curve falls, so the marginal product of an extra hour falls. The marginal product is diminishing. At 4 hours per day the average product is The average product falls as we move along the curve.

At each point the marginal product the slope of the curve is lower than the average product the slope of the ray. The marginal product at four hours of study is approximately 7, which is the increase in the grade from one more hour of study. More precisely, the marginal product is the slope of the tangent at that point, which is slightly higher than 7. At each point on the production function, the marginal product is the increase in the grade from studying one more hour. The marginal product corresponds to the slope of the production function.

Leibniz: Average and marginal productivity. The model captures the idea that an extra hour of study helps a lot if you are not studying much, but if you are already studying a lot, then studying even more does not help very much.

Leibniz: Diminishing marginal productivity. A production function with this shape is described as concave. Leibniz: Concave and convex functions. This happens because the marginal product is diminishing: each hour is less productive than the ones that came before.

And it implies that the average product is also diminishing: each additional hour of study per day lowers the average product of all his study time, taken as a whole. This is another example of the diminishing average product of labour that we saw in Unit 2.

In that case, the average product of labour in food production the food produced per worker fell as more workers cultivated a fixed area of land. Lastly, notice that if Alexei was already studying for 15 hours a day, the marginal product of an additional hour would be zero.

Studying more would not improve his grade. Marginal change is an important and common concept in economics. You will often see it marked as a slope on a diagram. With a production function like the one in Figure 3. We have said that when Alexei studies for 4 hours a day the marginal product is 7, the increase in the grade from one more hour of study.

Because the slope of the curve changes between 4 and 5 hours on the horizontal axis, this is only an approximation to the actual marginal product. More precisely, the marginal product is the rate at which the grade increases, per hour of additional study. In this unit, we will use approximations so that we can work in whole numbers, but you may notice that sometimes these numbers are not quite the same as the slopes.

The marginal product is the rate of change of the grade at 4 hours of study. Suppose Alexei has been studying for 4 hours a day, and studies for 1 minute longer each day a total of 4. Then, according to the graph, his grade will rise by a very small amount—about 0.

A more precise estimate of the marginal product the rate of change would be:. If we looked at smaller changes in study time even further the rise in grade for each additional second of study per day, for example we would get closer to the true marginal product, which is the slope of the tangent to the curve at 4 hours of study.

If Alexei has the production function shown in Figure 3. The decision depends on his preferences —the things that he cares about. If he cared only about grades, he should study for 15 hours a day.

But, like other people, Alexei also cares about his free time—he likes to sleep, go out or watch TV. So he faces a trade-off: how many percentage points is he willing to give up in order to spend time on things other than study? We illustrate his preferences using Figure 3. Free time is defined as all the time that he does not spend studying. Every point in the diagram represents a different combination of free time and final grade.

Given his production function, not every combination that Alexei would want will be possible, but for the moment we will only consider the combinations that he would prefer.

Suppose he says he is indifferent between A and D, meaning he would feel equally satisfied with either outcome. We say that these two outcomes would give Alexei the same utility. How many points would you be willing to sacrifice for an extra hour of free time? Then we know that he is indifferent between A and E 16 hours, 75 points. Then we could ask the same question about combination E, and so on until point D.

Eventually we could draw up a table like the one in Figure 3. Alexei is indifferent between A and E, between E and F, and so on, which means he is indifferent between all of the combinations from A to D. The combinations in the table are plotted in Figure 3. Combinations A and B both deliver a grade of 84, but Alexei will prefer A because it has more free time. At combinations C and D Alexei has 20 hours of free time per day, but he prefers D because it gives him a higher grade.

Alexei says that F is another combination that would give him the same utility as A and E. By asking more questions, we discover that Alexei is indifferent between all of the combinations between A and D. Indifference curves can be drawn through any point in the diagram, to show other points giving the same utility. We can construct other curves starting from B or C in the same way as before, by finding out which combinations give the same amount of utility.

If you look at the three curves drawn in Figure 3. The curve through C gives the lowest utility of the three. In other models, these will often be consumption goods such as food or clothing, and we refer to the person as a consumer. Notice that:. If he is at A, with 15 hours of free time and a grade of 84, he would be willing to sacrifice 9 percentage points for an extra hour of free time, taking him to E remember that he is indifferent between A and E.

We have drawn the indifference curves as becoming gradually flatter because it seems reasonable to assume that the more free time and the lower the grade he has, the less willing he will be to sacrifice further percentage points in return for free time, so his MRS will be lower. You can see that, when Alexei has more free time and a lower grade, the MRS—the number of percentage points he would give up to get an extra hour of free time—gradually falls.

The diagram shows three indifference curves for Alexei. The curve furthest to the left offers the lowest satisfaction. He would be willing to move from A to E, giving up 9 percentage points for an extra hour of free time.

His marginal rate of substitution is 9. The indifference curve is steep at A. At H he is only willing to give up 4 points for an extra hour of free time. His MRS is 4. As we move down the indifference curve, the MRS diminishes, because points become scarce relative to free time. The indifference curve becomes flatter.

Look at the combinations with 15 hours of free time. On the lowest curve the grade is low, and the MRS is small. Alexei would be willing to give up only a few points for an hour of free time. As we move up the vertical line the indifference curves are steeper: the MRS increases. Now look at all the combinations with a grade of On the curve furthest to the left, free time is scarce, and the MRS is high. As we move to the right along the red line he is less willing to give up points for free time.

The MRS decreases—the indifference curves get flatter. The MRS is just the slope of the indifference curve, and it falls as we move to the right along the curve. If you think about moving from one point to another in Figure 3. When free time is scarce relative to grade points, Alexei is less willing to sacrifice an hour for a higher grade: his MRS is high and his indifference curve is steep. As the analysis in Figure 3. For a given amount of free time, Alexei is willing to give up more grade points for an additional hour when he has a lot of points compared to when he has few for example, if he was in danger of failing the course.

By the time you reach A, where his grade is 84, the MRS is high; grade points are so plentiful here that he is willing to give up 9 percentage points for an extra hour of free time. Leibniz: Indifference curves and the marginal rate of substitution. You can see the same effect if you fix the grade and vary the amount of free time. If you move to the right along the horizontal line for a grade of 54, the MRS becomes lower at each indifference curve.

As free time becomes more plentiful, Alexei becomes less and less willing to give up grade points for more time. In the diagram below, IC 1 is an indifference curve joining all the combinations that give the same level of utility as A. Combination B is not on IC 1. Your future employer then says that you will work for 40 hours per week leaving you with hours of free time per week.

Alexei faces a dilemma: we know from looking at his preferences that he wants both his grade and his free time to be as high as possible. But given his production function, he cannot increase his free time without getting a lower grade in the exam. Another way of expressing this is to say that free time has an opportunity cost : to get more free time, Alexei has to forgo the opportunity of getting a higher grade. In economics, opportunity costs are relevant whenever we study individuals choosing between alternative and mutually exclusive courses of action.

When we consider the cost of taking action A we include the fact that if we do A, we cannot do B. This is called an opportunity cost because doing A means forgoing the opportunity to do B.

In a nearby park there is concert B, which is free but happens at the same time. This is the opportunity cost of going to concert A. Because it is not their job. Accountants are paid to keep track of money, not to provide decision rules on how to choose among alternatives, some of which do not have a stated price.

But making sensible decisions and predicting how sensible people will make decisions involve more than keeping track of money. An accountant might argue that the park concert is irrelevant:. In Unit 2, we said that if an action brings greater net benefits than the next best alternative, it yields an economic rent and you will do it.

Another way of saying this is that you receive an economic rent from taking an action when it results in a benefit greater than its economic cost the sum of out-of-pocket and opportunity costs. With this information, what can we say? The British government introduced legislation in that gave universities the option to raise their tuition fees.

Does this mean that the cost of going to university has tripled? Think about how an accountant and an economist might answer this question. Ignore student loans. Free time has an opportunity cost in the form of lost percentage points in his grade equivalently, we might say that percentage points have an opportunity cost in the form of the free time Alexei has to give up to obtain them.

But before we can describe how Alexei resolves his dilemma, we need to work out precisely which alternatives are available to him. To answer this question, we look again at the production function. This time we will show how the final grade depends on the amount of free time, rather than study time. There are 24 hours in a day. Alexei must divide this time between studying all the hours devoted to learning and free time all the rest of his time.

If Alexei studies solidly for 24 hours, that means zero hours of free time and a final grade of If he chooses 24 hours of free time per day, we assume he will get a grade of zero. If we think of him choosing to consume a combination of these two goods, the curved line in Figure 3.

It represents his feasible frontier : the highest grade he can achieve given the amount of free time he takes. This curve is called the feasible frontier. It shows the highest final grade Alexei can achieve given the amount of free time he takes.

With 24 hours of free time, his grade would be zero. By having less free time, Alexei can achieve a higher grade. If Alexei chooses 13 hours of free time per day, he can achieve a grade of Therefore B is an infeasible combination of hours of free time and final grade. The maximum grade Alexei can achieve with 19 hours of free time per day is Combination D is feasible, but Alexei is wasting time or points in the exam. He could get a higher grade with the same hours of study per day, or have more free time and still get a grade of The area inside the frontier, together with the frontier itself, is called the feasible set.

A set is a collection of things—in this case all the feasible combinations of free time and grade. At combination A Alexei could get an extra hour of free time by giving up 3 points in the exam. The opportunity cost of an hour of free time at A is 3 points. The more free time he takes, the higher the marginal product of studying, so the opportunity cost of free time increases. At C the opportunity cost of an hour of free time is higher than at A: Alexei would have to give up 7 points.

The opportunity cost of free time at C is 7 points, corresponding to the slope of the feasible frontier. Any combination of free time and final grade that is on or inside the frontier is feasible.

On the other hand, even though a combination lying inside the frontier is feasible, choosing it would imply Alexei has effectively thrown away something that he values. If he studied for 14 hours a day, then according to our model, he could guarantee himself a grade of But he could obtain a lower grade 70, say , if he just stopped writing before the end of the exam.

It would be foolish to throw away points like this for no reason, but it would be possible. Another way to obtain a combination inside the frontier might be to sit in the library doing nothing—Alexei would be taking less free time than is available to him, which again makes no sense.

By choosing a combination inside the frontier, Alexei would be giving up something that is freely available—something that has no opportunity cost. He could obtain a higher grade without sacrificing any free time, or have more time without reducing his grade. It represents the trade-off he must make between grade and free time. At any point on the frontier, taking more free time has an opportunity cost in terms of grade points foregone, corresponding to the slope of the frontier.

Another way to express the same idea is to say that the feasible frontier shows the marginal rate of transformation : the rate at which Alexei can transform free time into grade points.

Look at the slope of the frontier between points A and E in Figure 3. Note that the slope of AE is only an approximation to the slope of the frontier. More precisely, the slope at any point is the slope of the tangent, and this represents both the MRT and the opportunity cost at that point. Leibniz: Marginal rates of transformation and substitution. As we shall see in the next section, the choice Alexei makes between his grade and his free time will strike a balance between these two trade-offs.

Look at Figure 3. Free time per day is given by 24 hours minus the hours of study per day. What can we conclude? The final step in this decision-making process is to determine the combination of final grade and free time that Alexei will choose.

Recall that the indifference curves indicate what Alexei prefers, and their slopes shows the trade-offs that he is willing to make; the feasible frontier is the constraint on his choice, and its slope shows the trade-off he is constrained to make.

IC 4 represents the highest level of utility because it is the furthest away from the origin. No combination of grade and free time on IC 4 is feasible, however, because the whole indifference curve lies outside the feasible set. Suppose that Alexei considers choosing a combination somewhere in the feasible set, on IC 1.

By working through the steps in Figure 3. On the indifference curve IC 1 , all combinations between A and B are feasible because they lie in the feasible set. Suppose Alexei chooses one of these points. All combinations in the lens-shaped area between IC 1 and the feasible frontier are feasible, and give higher utility than combinations on IC 1. Switching from B to D would raise his utility by an equivalent amount. But again, Alexei can raise his utility by moving into the lens-shaped area above IC 2.

He can continue to find feasible combinations on higher indifference curves, until he reaches E. At E, he has 19 hours of free time per day and a grade of Alexei maximizes his utility: he is on the highest indifference curve obtainable, given the feasible frontier.

At E the indifference curve is tangent to the feasible frontier. The marginal rate of substitution the slope of the indifference curve is equal to the marginal rate of transformation the slope of the frontier. Alexei maximizes his utility at point E, at which his indifference curve is tangent to the feasible frontier.

The model predicts that Alexei will:. We can see from Figure 3. At E, the slope of the indifference curve is the same as the slope of the feasible frontier. Now, remember that the slopes represent the two trade-offs facing Alexei:.

Alexei achieves the highest possible utility where the two trade-offs just balance E. His optimal combination of grade and free time is at the point where the marginal rate of transformation is equal to the marginal rate of substitution.

At B and D, the number of points Alexei is willing to trade for an hour of free time MRS is greater than the opportunity cost of that hour MRT , so he prefers to increase his free time. Remember, scarcity depends on both his preferences and the production function.

Suppose that all students have the same feasible frontier, but their indifference curves may differ in shape and slope depending on their preferences. The question he raised was: how would we cope with all of the additional leisure time? As we saw in Unit 2, new technologies raise the productivity of labour. We now have the tools to analyse the effects of increased productivity on living standards, specifically on incomes and the free time of workers.

We now apply our model of constrained choice to Angela, a self-sufficient farmer who chooses how many hours to work. We assume that Angela produces grain to eat and does not sell it to anyone else. In economics, trade-off means the exchange, in which a person sacrifices one or more things for getting a particular product, service or experience. It refers to all the courses of action which could be employed, other than the present one.

It is a deal, that arises as a compromise, wherein to obtain a certain aspect we have to lose another aspect. In other words, while making a selection, we have to accept less of something, for obtaining more of something else, the outcome would be trade-offs. For example : Suppose a company wants to start a project, which requires huge investment and other resources, so the trade-off entails the reduction in certain expenses, in order to invest more in the new project.

Hence, tradeoff implies the way of forsaking one or more desirable alternatives, in return for obtaining a specified outcome. Opportunity cost or alternative cost, as the name suggest, is the cost of opportunity lost, i. It is the actual return of the forsaken alternative, which cannot be obtained, due to the scarcity of resources.

As we know that resources are available to us, in a limited quantityr, but these resources have diverse uses, with varied returns. So, the resources are employed to the most productive use, by sacrificing the next best use of the resources. Hence, the opportunity cost is the amount of return that is expected to be generated when the resources are put to the second best alternative. For example : Suppose after pursuing MBA you have two options available to you.

One, to start your own business and earn 10 lakhs per annum or join a company and get 12 lakhs per annum. So, if you commence your own business you will earn 10 lakhs per year, but you will not get 12 lakhs. This 12 lakhs is your opportunity cost, which you will get for serving the company and not starting your own business. Therefore, what is valued more for an individual than any other thing, vary among individuals, while deciding the way in which resources are to be allocated.

Session Objectives :. Handouts and Supplemental Materials. What could you be doing instead of being here for this session? List your alternatives here. What is the Opportunity Cost for a high school student to study one hour for Economics?

What will confuse your students? We will continue the story of Adam and Eve in a later session. Economics builds on ideas! Benchmarks: grade 8: Scarcity is the condition of not being able to have all of the goods and services one wants. It exists because human wants for goods and services exceed the quantity of goods and services that can be produced using all available resources.

Like individual, governments and societies experience scarcity. Choices involve trading off the expected value of one opportunity against the expected value of its best alternative. The evaluation of choices and opportunity costs is subjective; such evaluations differ across individuals and societies.

Benchmarks: grade Marginal benefit is the change in total benefit resulting from an action. Marginal cost is the change in total cost resulting from an action.

As long as the marginal benefit of an activity exceeds the marginal cost, people are better off doing more of it; when the marginal cost exceeds the marginal benefit, they are better off doing less of it.

Benchmarks: grade 8: Scarcity requires the use of some distribution method, whether the method is selected explicitly or not. Session Objectives : Define scarcity as the fundamental economic condition, and provide examples of the importance and implications of relative scarcity. Develop the logic that leads from scarcity to the necessity of choice. Illustrate how the economic condition forces everyone — consumers and producers — to make choices.

Discuss how societies devise different systems of allocation to systematically address the necessity of choice. Demonstrate the subjectivity of distinctions between needs and wants. Discuss how allocation systems help people make choices. Illustrate the concepts of trade offs and opportunity cost. Introduce and practice the production possibility frontier model of trade-off and opportunity cost. Introduce marginal decision making. Illustrate and explain how economists distinguish between good choices and poor choices.

Scarcity exists when resources have more than one valuable use. Scarcity exists even in the midst of abundance.

Scarcity forces people to choose between alternatives. People choose purposefully from the alternatives they perceive. Scarcity is dealt with more effectively by recognizing that the distinction between needs and wants is subjective.