Week 1: Discussion: Opportunity Costs

Choose a recent purchase of yours to consider for your initial response to this Discussion prompt. Try to use an example in which the compromises were either clearly worth it—or clearly not worth it. Consider your reasons for making the purchase and how you weighed the pros and cons of your decision.Review the Academic Writing Expectations for 1000-Level Courses, provided in this week’s Learning Resources.Post a 150- to 225-word (2- to 3-paragraph) explanation of what the opportunity costs of your purchase were. In the end, was it worth it? Why or why not? To support your response, be sure to reference at least one properly cited scholarly source.

Assignment in Macroeconomics Class

I have to do two parts of a group assignment (B and D) Each part is 500-700 words (excluding references)Please note the following information regarding your assignment. -. Topic: Economy of Canada: strengths and weaknesses -. Word Limit: Between 500-700 (excluding graphs, tables and references, all sources must be included in reference section) Parts and Structure/format of the assignment: (My part here is b & d) a. Introduction (Background of Canadian Economy) b. Trend of Economic growth (Discussion on a10-15 year comparative economic growth performance), c. Recent Investment scenario both domestic and FDI d. Most prospective sectors of Canada e. Strengths and weaknesses of Canadian economy based on previous sections f. Summary and Conclusions g. Reference list.

solve four questions in attach marco enconomy

require in the attach easy questions ask me if you have any question. But you should be familiar with infer marco enconomy.OPTIONAL QUESTIONS – makeup (10 points) Due April 21
Show, using a sketch graph, a consumer who prefers a cash gift rather than a larger gift
of merchandise. [As a starting point use an optimal choice of a consumption bundle
containing an amount of good X and a composite good Y.]
Show, using a sketch graph, income and substitution effects of a price decrease for an
inferior good. Fully label your diagram.
Optional assignment 2 (10 points)
1. A perfectly competitive firm has a short run total cost given by:
TC = 100+2Q+Q2
With a marginal cost MC = 2+2Q
Find average total cost and average variable cost as a function of output
If P=25, how much will the firm produce in the short run?
If P=20, how much will the firm produce in the short run?
Assuming that the firm has the same average total cost curve in the long run how much will
it produce in the long run?
2. A firm has marginal costs given by MC=10+Q and average variable costs AVC= 10+Q/2
If fixed costs are $5000 and the market price is $100 find firm’s maximum profit. Will the firm
continue to operate in the short run? Explain.
3. Sketch a natural monopoly firm under marginal cost pricing regulation. Label its price, quantity,
and profit. What is the deadweight loss (loss in consumer and producer surplus) if regulation is

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Answer the question

Question 1Suppose that a state raises its minimum wage from $8/hour to $13/hour. Using an isocost-isoquant diagram, show how this will affect labor demand of a firm which produces Q = 200 units of output each month using two inputs: low-skilled labor and capital. Please label and explain your diagram completely. Question 2Susan consumes two goods, bananas and toast. The price of a banana is $0.30 and the price of a slice of toast is $0.15. Suppose that with her current consumption, Susan’s marginal utility from the last banana she consumes is 12 while her marginal utility from the last piece of toast is 3. Is Susan currently maximizing utility? If not, how should Susan adjust her consumption to maximize utility?

Read the Economic paper then answer the question.

After read the paper, briefly list and explain 3-4 key features in this paper, Try to organize your discussion around 3-4
issues.Does Schooling Cause Growth?
A number of economists find that growth and schooling are highly correlated across
countries. A model is examined in which the ability to build on the human capital
of one’s elders plays an important role in linking growth to schooling. The model
is calibrated to quantify the strength of the effect of schooling on growth by using
evidence from the labor literature on Mincerian returns to education. The upshot is
that the impact of schooling on growth explains less than one-third of the empirical
cross-country relationship. The ability of reverse causality to explain this empirical
relationship is also investigated. (JEL I2, J24, O4)
Robert J. Barro (1991), Jess Benhabib and
Mark M. Spiegel (1994), Barro and Xavier
Sala-i-Martin (1995), Sala-i-Martin (1997), and
many others find schooling to be positively correlated with the growth rate of per capita GDP
across countries. For example, we show below
that greater schooling enrollment in 1960 consistent with one more year of attainment is
associated with 0.30-percent faster annual
growth over 1960 –1990. This result is consistent with models, such as that of Barro et al.
(1995), in which transitional differences in
human-capital growth rates explain temporary
differences in country growth rates.
We examine a model with finite-lived individuals in which human capital can grow with
rising schooling attainment and thereby contribute to a country’s growth rate. Each generation
learns from previous generations; the ability to
build on the human capital of one’s elders plays
an important role in the growth generated by
rising time spent in school. We also incorporate
into the model a positive externality from the
level of human capital onto the level of technology in use.
We calibrate the model to quantify the
strength of the effect of schooling on growth.
To do so, we introduce a measure of the impact
of schooling on human capital based on exploiting Mincerian returns to education and experience (Jacob Mincer, 1974) commonly estimated
in the labor literature.1 Our calibration requires
that the impact of schooling on human capital
be consistent with the average return to schooling observed in estimates of the Mincer equation conducted on micro data across 56 separate
countries. We also require that the humancapital returns to schooling exhibit diminishing
returns consistent with the observed higher returns to schooling in countries with low levels
of education. We further discipline the calibration by requiring that average human-capital
growth not be so high that technological regress
must have occurred on average in the world
over 1960 –1990. Our principal finding is that
the impact of schooling on growth probably
explains less than one-third of the empirical
cross-country relationship, and likely much less
than one-third. This conclusion is robust to allowing a positive external benefit from human
capital to technology.
If high rates of schooling are not generating
higher growth, what accounts for the very
strong relationship between schooling enrollments and subsequent income growth? One element is that countries with high enrollment
* Bils: Department of Economics, Harkness Hall, University of Rochester, Rochester, NY 14627; Klenow: Research Department, Federal Reserve Bank of Minneapolis,
90 Hennepin Avenue, Minneapolis, MN 55480. We are
grateful to Yongsung Chang and three referees, particularly
the final referee, for useful comments. Saasha Celestial-One
provided excellent research assistance.
Our approach is very related to the work of Anne O.
Krueger (1968), Dale W. Jorgenson (1995), and Alwyn
Young (1995), each of whom measures growth in worker
quality in a particular country based on the relative wages
and changing employment shares of differing schoolingand age-groups. Our approach is more parametric, but can
also be applied to many more countries.
VOL. 90 NO. 5
rates in 1960 exhibit faster rates of growth in
labor supply per capita from 1960 to 1990. This
explains perhaps 30 percent of the projection of
growth on schooling. A second possibility is
that the strong empirical relation between
schooling and growth reflects policies and other
factors omitted from the analysis that are associated both with high levels of schooling and
rapid growth in total factor productivity (TFP)
from 1960 to 1990. For example, better enforcement of property rights or greater openness
might induce both faster TFP growth and higher
school enrollments. Finally, the relationship
could reflect reverse causality, that is, schooling
could be responding to the anticipated rate of
growth for income.
To explore the potential for expected growth to
influence schooling, we extend the model to incorporate a schooling decision. Our model builds
on work by Gary S. Becker (1964), Mincer
(1974), and Sherwin Rosen (1976). A primary
result is that anticipated growth reduces the effective discount rate, increasing the demand for
schooling. Schooling involves sacrificing current
earnings for a higher profile of future earnings.
Economic growth, even of the skill-neutral variety, increases the wage gains from schooling.2
Thus an alternative explanation for the Barro et al.
findings is that growth drives schooling, rather
than schooling driving growth. We calibrate the
model to quantify the potential importance of the
channel from growth to schooling, again disciplined by estimates of empirical Mincer equations.
Our calibration suggests that expected growth
could have a large impact on desired schooling.
We conclude that the empirical relationship
documented by Barro and others does not primarily reflect the impact of schooling on
growth. We suggest that it may partly reflect the
impact of growth on schooling. Alternatively,
an important part of the relation between
schooling and growth may be omitted factors
that are related both to schooling rates in 1960
and to growth rates for the period 1960 to 1990.
The rest of the paper proceeds as follows. In
Section I we lay out the model. In Section II we
Andrew D. Foster and Mark R. Rosenzweig (1996) find
evidence for a channel from growth to schooling that involves
skill-bias of the technical change. They document that Indian
provinces benefiting from the Green Revolution in the 1970’s
saw increases in returns to, and enrollment in, schooling.
document that a higher level of schooling enrollment is associated with faster subsequent
growth in GDP per capita (also GDP per
worker, and GDP per worker net of physical
capital accumulation). In Section III we calibrate the model and explore whether the channel from schooling to human-capital growth is
capable of generating the empirical coefficient
found in Section II. In Section IV we add the
channel from schooling to the level of technology, to see whether the effect of schooling on
human capital and technology combined can
mimic the empirical relationship. In Section V
we investigate whether the reverse channel from
expected growth to schooling can do the same.
In Section VI we conclude.
I. A Model of Schooling and Growth with
Finite-Lived Individuals
A. The Channel from Schooling to Growth
We start with production technologies since
much of our estimation and calibration is based
solely on them, with no assumptions needed
about preferences or capital markets. Consider
an economy with the production technology
Y共t兲 ⫽ K共t兲 ␣ 关A共t兲H共t兲兴 1 ⫺ ␣
where Y is the flow of output, K is the stock of
physical capital, A is a technology index, and H
is the stock of human capital. The aggregate
stock of human capital is the sum of the humancapital stocks of working cohorts in the economy. For exposition, suppose for the moment
that all cohorts go to school from age 0 to age s
(so that s is years of schooling attained) and
work from age s to age T. Then we have
H共t兲 ⫽

h共a,t兲L共a,t兲 da
where L(a,t) is the number of workers in cohort
a at time t and h(a,t) is their level of human
capital. Note the efficiency units assumption
that different levels of human capital are perfectly substitutable. We generalize (2) to the
case where s and T differ across cohorts.
We posit that individual human-capital
stocks follow
(3) h共a,t兲 ⫽ h共a ⫹ n,t兲 ␾ e f共s兲 ⫹ g共a ⫺ s兲 @a ⬎ s.
The parameter ␾ ⱖ 0 captures the influence of
teacher human capital, with the cohort n years
older being the teachers. When ␾ ⬎ 0 the quality of schooling is increasing in the human
capital of teachers.3 The exponential portion of
(3) incorporates the worker’s years of schooling
(s) and experience (a ⫺ s), with f⬘(s) ⬎ 0 and
g⬘(a ⫺ s) ⬎ 0 being the percentage gains in
human capital from each year. Note that the
“teachers” that influence h are at school and on
the job. In the special case of ␾ ⫽ 1, h grows
from cohort to cohort even if years of schooling
attained are constant, à la Robert E. Lucas, Jr.
(1988) and Sergio Rebelo (1991). If ␾ ⬍ 1, then
growth in h from cohort to cohort requires rising s and/or T.
When ␾ ⫽ 0, f(s) ⫽ ␪ s, and g(a ⫺ s) ⫽
␥ 1 (a ⫺ s) ⫹ ␥ 2 (a ⫺ s) 2 , equation (3) reduces
to the common Mincer (1974) specification.
This specification implies that the log of the
individual’s wage is linearly related to that individual’s years of schooling, years of experience, and years of experience squared. We
choose this exponential form precisely so that
we can draw on the large volume of micro
evidence on ␪, ␥1, and ␥2 to quantify the impact
of schooling on human capital and growth. This
approach differs from that of N. Gregory
Mankiw et al. (1992), who assume a humancapital production technology identical to that
of other goods (consumption and physical capital). Although (3) is a departure from the prior
literature, we view it as an improvement because it ensures that our estimates of human
capital are consistent with the private returns to
schooling and experience seen in micro data.4
In addition to the direct effect of human cap-
We ignore nonlabor inputs because evidence suggests
that teacher and student time constitute about 90 percent of
all costs (see John W. Kendrick [1976] and U.S. Department
of Education [1996]).
Recent papers that have followed our approach include
Charles I. Jones (1998), Boyan Jovanovic and Raphael Rob
(1998), Jonathan Temple (1998), Daron Acemoglu and Fabrizio Zilibotti (1999), and Robert E. Hall and Jones (1999).
ital on output in (1), human capital may affect
output by affecting A, the level of technology.
Richard R. Nelson and Edmund S. Phelps
(1966), Theodore W. Schultz (1975), Benhabib
and Spiegel (1994), and many others propose
that human capital speeds the adoption of technology. For instance, the growth rate of technology for country i may follow
A i 共t兲
g A i 共t兲 ⫽ ⫺␩ ln ៮
A 共t兲
⫹ ␤ ln h i 共t兲 ⫹ ␰ i 共t兲
where A៮ is the exogenously growing “world technology frontier” and hi(t) ⫽ Hi(t)/Li(t) is the average level of human capital in country i.5 When
␩ ⬎ 0, the closer the country’s technology to the
frontier the slower the country’s growth rate.
When ␤ ⬎ 0, the higher the country’s human
capital the faster the country’s growth rate. As
stated, one motivation for ␤ ⬎ 0 is that human
capital may speed technology adoption. But another motivation is that human capital may be
necessary for technology use. That is, in (4)⬘ human capital can be indexing the fraction of frontier
technology which the country can use.6 Evidence
that human capital plays a role in adoption includes Finis Welch (1970), Ann Bartel and Frank
Lichtenberg (1987), and Foster and Rosenzweig
(1996). Empirical studies finding that human capital is complementary to technology use are plentiful, recent examples being Mark Doms et al.
(1997), David H. Autor et al. (1998), and Eli
Berman et al. (1998).
If one integrates (4)⬘ over time one finds that
the level of technology in a country should be a
positive function of its current and past humancapital stocks. Below we report that there is
ample evidence that the level of technology [A
constructed from equation (1)] and the level of
human capital [constructed using equation (3)]
are positively correlated across countries. Conditional on current human capital, however, we
do not find a positive correlation between current A and past human capital. In terms of (4)⬘,
L i (t) is the sum of L i (a, t) across cohorts.
William Easterly et al. (1994), Jones (1998), and Francisco Caselli (1999) adopt this “use” formulation.
VOL. 90 NO. 5
this could mean that ␩ is very high so that
transition dynamics are rapid and economies are
close to their steady-state paths. This would
suggest a simple use formulation, with a higher
level of human capital allowing a higher level of
technology use:
ln A i 共t兲 ⫽ ␤ ln h i 共t兲 ⫹ ln A៮ 共t兲 ⫹ ␰ i 共t兲.
g A i 共t兲 ⫽ ␤ g h i 共t兲 ⫹ g A៮ 共t兲 ⫹ ␧ i 共t兲.
Equation (5) says that growth in human capital
contributes to growth indirectly (through growth
in A), not just directly [through H in equation (1)].
Note that, because we measure h to be consistent
with Mincerian private-return estimates in (3), this
indirect effect of human capital on technology
represents an externality not captured by the individual worker. Externalities might arise because
of learning from others who have adopted or because introduction of technology is based on the
amount of human capital in the country as a whole
(e.g., when there is a fixed cost component to
transferring technology).
In Section III we estimate the effect of
schooling on growth using equations (1)
through (5), eschewing (4)⬘ in favor of (4) because the latter fits the data better. In conducting
this growth accounting we can take schooling
decisions as given (i.e., as data). To quantify
possible reverse causality, however, we must
model schooling decisions. For this purpose, we
next specify market structure and preferences.
B. The Channel from Growth to Schooling
The common r assumption means that, in our model,
the private rate of return to schooling will be equalized
across countries. This is in contrast to the model of Barro et
al. (1995), in which low schooling countries have high
returns to human capital but cannot borrow to finance
human-capital accumulation.
␣ Y共t兲/K共t兲 ⫽ r ⫹ ␦
共1 ⫺ ␣ 兲Y共t兲/H共t兲 ⫽ w共t兲
where ␦ is the depreciation rate of physical
capital and w is the wage rate per unit of human
capital. Combining (1), (6), and (7), one can
easily show that
which means the wage per unit of human capital
grows at the rate g A .
In this economy each individual is finitelived and chooses a consumption profile and
years of schooling to maximize

e ⫺␳t
c共t兲 1 ⫺ 1/ ␴
dt ⫹
1 ⫺ 1/ ␴

e ⫺ ␳ t ␨ dt.
Here c is consumption and ␨ is flow utility from
going to school. Schultz (1963) and others argue that attending class is less onerous than
working, especially in developing countries.
This benefit of going to school will create an
income effect on the demand for schooling.8
The individual’s budget constraint is

We consider a competitive open economy
facing a constant world real interest rate r. 7
With the price of output in the world normalized
to one each period, firm first order conditions
from (1) are
e ⫺rt w共t兲h共t兲 dt ⱖ

e ⫺rt c共t兲 dt

e ⫺rt ␮ w共t兲h共t兲 dt
We model a utility flow from going to school for
concreteness, but there are other motivations for an income
effect: higher education may improve one’s ability to enjoy
consumption throughout life (Schultz, 1963); higher income
may relax borrowing constraints; and tuition may not rise
fully with a country’s income (say because goods are used
in education production).
where ␮ ⬎ 0 is the ratio of school tuition to the
opportunity cost of student time.9 Individuals
go to school until age s and work from age s
through age T.
From (3), (9), and (10), the first-order condition for an individual’s schooling choice is
(11) 共1 ⫹ ␮ 兲w共s兲h共s兲 ⫽ ␨ c共s兲 1/ ␴

e ⫺r共t ⫺ s兲 关f⬘共s兲 ⫺ g⬘共t ⫺ s兲兴w共t兲h共t兲 dt
which equates the sum of tuition and the opportunity cost of student time for the last year spent
in school (the left-hand side) to the sum of the
utility flow from attending plus the present
value of future earnings gains (the right-hand
side). The gap between human capital gained
from education and that gained from experience
[ f⬘(s)⫺g⬘(t⫺s)] enters because staying in
school means forgoing experience.
The privately optimal quantity of schooling is
generally not an explicit function of the model’s
parameters. To illustrate concepts, however,
consider a special case in which it is: f(s) ⫽ ␪ s,
g(a ⫺ s) ⫽ ␥ (a ⫺ s), and ␨ ⫽ 0. (Later, when
we calibrate the model, we consider ␨ ⬎ 0 and
g and f functions with realistic curvature in s
and a ⫺ s.) Using h(t) ⫽ h(s)e ␥ (t ⫺ s) @t ⬎ s,
w(t) ⫽ w(s)e g A(t ⫺ s) from (8), and first-order
condition (11), the privately optimal quantity of
schooling is
(12) s ⫽ T

r ⫺ gA ⫺ ␥
⫻ ln

␪ ⫺ ␥ ⫺ ␮ 共r ⫺ g A ⫺ ␥ 兲
Equation (12) illustrates the channel by which
higher expected growth in A can induce more
schooling. The interest rate r and the growth
rate g A enter the schooling decision through
We make tuition costs increasing in the opportunity
cost of student time because, in the data, tuition rises with
the level of education (see U.S. Department of Education,
their difference (r ⫺ g A ), so comparative statics of the schooling decision with respect to g A
mirror those for r, with the opposite sign.
Higher growth acts just like a lower market
interest rate: by placing more weight on future
human capital, it induces more schooling. The
benefit of having human capital is proportional
to the level of A while working. The cost of
investing in human capital is proportional to the
level of A while in school. Thus higher A in the
future relative to today, which is to say higher
growth in A, raises the private return to investing in schooling.
Other noteworthy implications of the model
are as follows. A permanently higher level of
technology A (equivalently, wage per unit of
human capital) does not affect the optimal
amount of schooling because it affects the marginal cost and benefit of schooling in the same
proportion. Similarly, neither teacher human
capital nor its contribution to learning (␾) affect
the schooling decision. These results on A and
teacher human capital hinge on ␨ ⫽ 0 (no utility
benefit to attending class). Regardless of the
level of ␨, a higher life expectancy (T) results in
more schooling, since it affords a longer working period over which to reap the wage benefits
of schooling. Likewise, a higher tuition ratio (␮)
lowers schooling.
II. The Cross-Country Pattern of Schooling
and Growth
Barro (1991) finds that 1960 primary- and
secondary-school enrollment rates are positively correlated with 1960 –1985 growth in real
per capita GDP. Column (1) of our Table 1 reproduces this finding using updated Robert
Summers and Alan Heston (1991) Penn World
Tables Mark 5.6 data and Barro and Jong-Wha
Lee (1993) enrollment rates.10 Our measure of
schooling equals six times a country’s primaryschool enrollment rate plus six t…
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