StudySpace: Economics in Development, 6th Edition

Worked Example: Private versus Social Rates of Return

To evaluate the rate of return to education, one must calculate the discounted present value of lifetime earnings. To simplify this cumbersome task, let us assume that people live for only two “years”: youth (year 1) and adulthood (year 2). Youths either go to school or work. If they go to school then they earn zero, but if they work they earn $1,000. As adults, everyone works. An educated adult earns $3,500, while an uneducated adult earns only $2,000. Individuals therefore choose between two alternative lifetime earnings profiles:

The benefit of going to school is the present discounted value of the earnings stream so generated. Note that the relevant figure consists of incremental earnings that accrue from going to school. In year 2, this amounts to $1,500. In year 1 the earnings “gain” is actually –$1,000. The foregone earnings in year 1 can be treated as an implicit cost, or it can be incorporated in the calculation of the earnings gain from schooling as a negative gain. The overall result is the same either way. Here, we use the latter approach in order to be consistent in defining the benefit each year as incremental earnings.

To avoid ambiguity and simplify the calculation, let earnings be paid at the beginning of each year; thus, earnings for year 1 do not need to be discounted, while earnings for year 2 are discounted by a factor of (1 + r). The present discounted value of the benefits of schooling is

1 + r where r is an appropriate discount rate, in decimal units. For example, if r = 0.10, then 1,500

Now what about costs of schooling? There are both implicit and explicit costs to consider. The implicit cost consists of the earnings foregone by going to school instead of working. This opportunity cost was taken into account above. As for the explicit cost, we will assume that the cost of providing schooling is $400 per student per year and that the government provides a subsidy to cover this full amount. Under these conditions the net benefit of schooling, as far as the individual is concerned, is V as defined above.

The private rate of return is defined as the discount rate for which the present value of net benefits equals zero. This is the effective yield earned on the investment in education. It is not hard to see that the private rate of return in this case is 50 percent. You “invest” $1,000 (in foregone earnings) to get back $1,500 a year later. In terms of the mathematics, V = 0 can be solved to find r = 0.5 = 50 percent.

To calculate the social rate of return, all the costs must be taken into account, whether borne by the individual or by the government. Factoring in the explicit cost of $400, the net social benefit in year 1 equals –$1,400. For year 2, the net social benefit is +$1,500, representing the extra national product generated by the investment in education. To calculate the social rate of return, one finds the value of r such that:

Looking at the social costs and benefits, an investment of $1,400 pays off $1,500 the following year. Solving the equation gives r = 0.0714 = 7.14 percent. This is the social rate of return. Since the social rate of return is only 7.14 percent, there are probably alternative investments that would be more productive than education in this case. Yet because of the subsidies, the private rate of return is 50 percent. Hence, the demand for education is likely to be very strong, despite the low social rate of return.

Exercises

1. It is your turn to calculate private and social rates of return on education. In Baccalauria, primary school is compulsory; further education is not. For simplicity, assume that people live for four “years”: a year in primary school (age 1), a year when they could be going to secondary school (age 2), a year when they could be in college (age 3), and a year where everyone is in the labor force (age 4). Each Baccalaurian chooses one of three alternative lifetime earnings options, summarized in Table 8–1.

Click here for Table 8-1

a. In Figure 8–2 draw the three lifetime earnings curves corresponding to the three options shown in the Table. Label the three curves A, B, and C, respectively.

b. Consider the choice of whether or not to attend secondary school.

(i) What are the incremental earnings one can expect from attending secondary school, compared to joining the labor market straight out of primary school?

Incremental earnings at age 2 = $ .

Incremental earnings at age 3 = $ .

Incremental earnings at age 4 = $ .

(ii) Would someone with a very high discount rate, say 40 percent, choose to go to secondary school? Explain. (Note that a high discount rate is characteristic of people in dire poverty, for whom deferment of income is very costly.)

c. Now consider the decision faced by a secondary-school graduate about whether to invest in a college education. On reaching age 3, the graduate must choose between going to work (option B) or going to college (option C). College costs $1,000, of which the government bears $500 and the individual pays $500.

(i) Looking at the investment in college education from the point of view of the individual, the net private benefit of attending college is

$ at age 3

$ at age 4.

Don’t forget to take into account the opportunity cost of foregoing income in year 3 to go to college, as well as the individual’s share of the explicit costs.

(ii) Write the equation for calculating the private rate of return to investment in a college education. Assume that the decision on college is made at the start of age 3, so that ages 3 and 4 correspond to years 0 and 1, respectively, in the present-value formula. Use r to represent the discount rate.

V = .

(iii) What is the private rate of return to investing in a college education? Remember, this is defined as the value of r
for which V = 0.

%.

d. Now evaluate the investment in college education from the point of view of society.

(i) Taking into account the $500 cost that is borne by the government, in addition to the $500 cost to the individual, the net social benefit of a college education is

$ at age 3

$ at age 4.

(ii) Write the equation for calculating the social rate of return to investment in a college education? Again use r to represent the discount rate.

V′ = .

(iii) What is the social rate of return to investing in a college education?

%.

2. There are pitfalls in using earnings data for cost-benefit analysis of investments in education. First, current data may not be a good indicator of future payoffs. In fact, the figures in Table 8–1 were published on the sports page of the Baccalaurian Times. This information convinced many high-school graduates to attend college that year. After all, the private rate of return to investment in higher education looked quite high. A year later, though, the flood of college graduates hit the labor market. This increase in supply caused average earnings for college graduates to fall to $4,500. All other earnings figures remained unchanged.

a. The drop in earnings for graduates meant that an investment in college education produced less of a benefit than people had expected.

(i) The net private benefit at age 4 of having a college education turned out to be just

$ .

(ii) The private rate of return on a college education turned out to be

%.

(iii) And the social rate of return on investment in a college education was

%.

(Hint: For the social rate of return you should get a very round number.)

b. A second problem is that it may be incorrect to infer from the data that education is the cause of higher earnings. An astute economist discovered that people who attend college are more industrious than people who don’t attend. He surmised that part of the observed wage differential is caused by the “screening” effect of a college degree, not a genuine productivity gain. The economist calculated that the same people, if they skipped college, would earn more anyway than the amounts shown for option B in Table 9–1. They would earn $1,600 at age 3 and $2,400 at age 4 without a degree, compared to $0 at age 3 and $4,500 at age 4 if they do attend college.

(i) If this analysis is valid, the net private benefit of a college education to these industrious citizens is actually

$ at age 3

$ at age 4.

(Don’t forget to include the explicit costs at age 3.)

(ii) The net social benefit of investing in a college education for these industrious citizens is

$ at age 3

$ at age 4.

 

(iii) What are the true private and social rates of return to investment in a college education in this case?

            Private rate of return = %

            Social rate of return = %

c. Compare the private and social rates of return calculated in part b above with the returns that you calculated in Exercise 1.  What do the differences imply about the accuracy of cost-benefit analysis?  What do you conclude about the efficiency of investing in higher education in Baccalauria?

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