While collecting old economics examination questions at the Harvard University Archives, I happened to come across a final examination for Political Economy from the pre-Dunbar years. The senior year course during the academic year 1868-69 was taught by Francis Bowen who assigned his own textbook, The Principles of Political Economy applied to the Condition, the Resources, and the Institutions of the American People (2nd edition, 1859). In the following year (1870) Bowen published American Political Economy; including Strictures of the Currency and the Finances since 1861. One probably can presume his lectures were closer to the latter of the two books.
For this post I have included Bowen’s obituary published by the Harvard Crimson as well as a summary of the Harvard College curriculum in 1868-69 as published in the annual report of the President of Harvard College.
__________________________
Bowen’s Examination Questions
POLITICAL ECONOMY.
- Explain the difference between the laws of England, France, and the United States in respect to the rights of inheritance and bequest of real estate and personal property, showing the economical results of each of the three systems.
- What are the Metayer system, the Allotment system, Tenant Right, the Cottier Tenure, Peasant Proprietors, and the advantages and disadvantages of each?
- Show the difference between Exchange Value, Market Price, and Cost of Production. What is the law of the Equation of Demand and Supply?
- Wherein does Monopoly or a Scarcity Value differ from ordinary Cost of Production? According to Ricardo, is Rent an element in the Cost of Production;–and why.
- How is the interchange of commodities between distant countries regulated not by their absolute, but their comparative, Cost of Production? Explain the Equation of International Demand, and show the influence of cost of carriage on International Values.
- By what is the Rate of Interest regulated? Does this Rate depend on the Value of Money? How does it affect the price of land?
- What are the fundamental rules of Taxation? Distinguish between Direct and Indirect taxation:–what provision in the Constitution of the United States on this subject? How ought this provision to affect the Income Tax?
- What effect has the Rate of Taxation on the amount of revenue collected? Ought taxes to be at the same rate on large and small incomes?
- When did the National Debts begin, and wherein do they differ from private debts? What is the Funding of a National Debt?
- How came both England and the United States to be in debt for a much larger amount than they ever received from their creditors? What are the arguments in favor of paying off a National Debt within the lifetime of the generation that contracted it?
Sen. Ann. June, 1869.
Source: Harvard University Archives. Harvard University, Final Examinations 1853-2001. Box 1, Folder “Final examinations, 1868-1869”.
__________________________
An Obituary for Francis Bowen
Late yesterday afternoon it was announced that Professor Francis Bowen had died at his home at one o’clock of heart failure. He was born on September 8, 1811, at Charleston, Mass., and was therefore in his seventy-ninth year. In 1833 he was graduated from the college in the same class with Professor Lovering, Professor Torrey, Dr. M. Wyman, Professor J. Wyman, and the late Dr. George E. Ellis of Boston. During the four years following his graduation he was an instructor here in intellectual philosophy and political economy. In 1843 he succeeded Dr. Palfrey as editor and proprietor of the North American Review which he conducted until 1854. He was appointed professor of history in the college in 1850, but the board of overseers refused to confirm the appointment on account of his unpopular views on politics. Three years later, however, he was unanimously confirmed as Alford professor to succeed Dr. Walker. In this capacity he continued to serve the college until December, 1889, when he resigned the professorship; so that he has been in active service over thirty-six years. He was a prompt and constant attendant at lectures and always interested in his work. Of late years he has done only half-work and is not well-known to many of the undergraduates. But his influence on the graduates has been remarkably strong, many of them remembering him with the greatest affection.
In the early days of the Lowell Institute he was one of the most popular lecturers in the country. In 1848-9 he lectured before the Institute on the application of metaphysical and ethical science to the evidences of religion; in 1850 on political economy; in 1852, on the origin and development of the English and American constitutions; and subsequently on English philosophers from Bacon to Sir William Hamilton. The most of these lectures were subsequently published. He also published an annotated edition of Virgil, Critical Essays on the History and Present Condition of Speculative Philosophy, Principles of Political Economy, a text book on Logic, Sir William Hamilton’s essays on metaphysics, condensed and edited, and not more than five years ago he prepared the report of the U. S. Silver Commission. In 1879 the degree of L. L. D. was conferred upon him by the University, an honor fifty crowning his years of usefulness. The last years of his life have been quiet and uneventful.
__________________________
Overview of Harvard College Courses of Instruction, 1868-69
APPENDIX.
I.
SUMMARY STATEMENT OF THE COURSE OF INSTRUCTION PURSUED IN THE SEVERAL DEPARTMENTS OF THE UNIVERSITY DURING THE ACADEMIC YEAR 1868-69.
I. ACADEMIC DEPARTMENT.
- RELIGIOUS INSTRUCTION.
INSTRUCTION in Ethics and in Christian Evidences was given by the Acting President. During the First Term he heard recitations from the Freshman Class, twice a week, in Champlin’s First Principles of Ethics, and Bulfinch’s Evidences of Christianity.
During the Second Term he met the Senior Class twice a week, hearing them recite in Peabody’s Christianity the Religion of Nature, and delivering Lectures on the Christian Scriptures and the Evidences of Christianity. During the entire year the service of Daily Prayers was attended by him; and he supplied the Chapel pulpit on Sunday.
Two hundred and seventy-five students had leave of absence from Cambridge to pass Sunday at home; one hundred and forty-five attended worship in the College Chapel; and one hundred and sixteen attended other churches in Cambridge.
- PHILOSOPHY.
The means of instruction in this Department are recitations familiarly illustrated at the time by the Professor, lectures occasionally substituted for recitations, and written forensic exercises.
The Department was under the charge of Francis Bowen, A. M., Alford Professor, assisted by William W. Newell, A.B., Instructor in Philosophy. During the First Academic Term the Senior Class recited three times a week in Bowen’s Ethics and Metaphysics, and Bowen’s Political Economy. During a portion of the Second Term the same Class recited twice a week in Bowen’s Ethics and Metaphysics. An elective section of the same class also recited three times a week in Mill’s Examination of Sir W. Hamilton’s Philosophy, Schwegler’s History of Philosophy, Mansel’s Limits of Religious Thought, and Bowen’s Essays. The Junior Class recited twice a week to Mr. Newell in Bowen’s Logic, Reid’s Essays, and Hamilton’s Metaphysics. The Sophomores recited to Mr. Newell twice a week during one term in Stewart’s Philosophy of the Mind.
Forensics were read, in the First Term, once a month by the Seniors, half of the Class attending each fortnight. The Juniors also read Forensics once a month during one term.
- RHETORIC AND ORATORY.
This Department is under the superintendence of Francis J. Child, Ph. D., Boylston Professor of Rhetoric and Oratory, assisted in the teaching of Elocution by James Jennison, A. M. Instruction was given to elective sections of the three higher classes in the Early English Language and Literature.
Sophomores had two lessons a week, and studied Vernon’s Anglo-Saxon Guide and Morris’s Specimens of Early English.
Juniors had three lessons a week, and studied Vernon’s Anglo-Saxon Guide, Morris’s Specimens, and Morris’s edition of the Prologues and Knightes Tale from Chaucer’s Canterbury Tales.
The Senior section read Thorpe’s Analecta Anglo-Saxoniea and Mätzner’s Altenglische Sprachproben.
One fifth of the Sophomore Class wrote Themes, and attended a critical exercise upon them, each week throughout the year.
The Juniors wrote Themes, and attended a critical exercise upon them, once every three weeks during the First Term.
The Senior Class had four Themes during the Second Term.
The inspection of performances for Commencement and for the other public Exhibitions is committed to this Department.
The foregoing statement relates to the duties of the Professor.
There are separate courses of instruction in Elocution, and in Reading, which are wholly under the care of the Tutor in Elocution.
The Sophomores and Freshmen attended him once every week during the year as required, and he gave instruction to extra sections from all the classes.
He superintended rehearsals of performances for the Public Exhibitions of the year; the final rehearsal for each of which is regularly attended by the Professor.
- HISTORY.
In this Department instruction was given to the whole Senior Class by Professor Torrey and Professor Gurney; the textbooks used being the Abridgment of Story’s Commentaries on the Constitution, Guizot’s Civilization in Europe, Arnold’s Lectures, and Hallam’s Middle Ages. An elective class read with Professor Torrey May’s Constitutional History and Mill on Representative Government. A special examination was held of students who had offered themselves as candidates for Honors after having pursued an additional course of study.
The Sophomore Class recited to Professor Gurney in “ The Student’s Gibbon ” during the First Term.
The Freshman Class recited to Mr. Lewis, in the Second Term, in Duruy’s “Histoire Grecque.”
- MODERN LANGUAGES.
This Department is under the superintendence of James R. Lowell, A. M., Smith Professor of the French and Spanish Languages, and Professor of Belles-Lettres. Elbridge J. Cutler, A. B., Assistant Professor, has special charge of the instruction in French and German. Bennett H. Nash, A. M., is instructor in Italian and Spanish. Thomas S. Perry, A. M., is Tutor of Modern Languages. Louis C. Lewis, A. M., was Tutor of Modern Languages during the last year.
French is a required study during the First Term of the Freshman year; and Ancient History is taught from a French textbook during the Second Term of that year. French is an elective study during the Senior year. German is a required study during the Sophomore year; and an elective during the Junior and Senior years. During the last year the Sophomores studied French instead of German, they having failed to study French during their Freshman year, for reasons given in the last Annual Report. Spanish is studied as an extra, i. e. without marks, during the Junior year, and as an elective during the Senior year. Italian is an elective in the Sophomore, Junior, and Senior years, and the students are allowed to study Italian during any one or two of these three years; but no Senior beginning Italian is allowed to receive marks for the same.
The Professor gave a course of lectures to the Seniors during the Second Term.
The Assistant Professor taught elective German to the Seniors in two sections, three times a week throughout the year. Text-books, Otto’s and Weisse’s German Grammars, “Egmont,” “Taugenichts,” “Braune Erica,” Schiller’s “Maria Stuart,” and Goethe’s “Wahrheit und Dichtung.” He also taught elective French to the Seniors in two sections, three times a week. Textbooks, Beaumarchais’s “Barbier de Seville,” La Fontaine’s Fables, Racine’s “Athalie,” “Selections from French Prose-Writers,” and Pylodet’s “ Littérature Française.”
Instruction was given in Italian as follows :—
To a section of the Senior Class, in three recitations a week. This section read portions of Tasso’s “Gerusalemme ” and of Dante’s “Divina Commedia,” upon which the Instructor gave explanatory lectures. The section also handed in written translations from English into Italian, and had exercises in writing Italian from dictation. They had one written examination beside the annual examination.
To a section of the Junior Class, in two recitations a week. The textbooks used were Cuore’s Grammar, Nota’s “La Fiera,” and Dall’ Ongaro’s “La Rosa dell’ Alpi.” They attended one private written examination, practised writing Italian from dictation, and gave in written translations from English into Italian.
To two sections of the Sophomore Class. Each section had two recitations a week in the same text-books as the Juniors. Each section was exercised in writing Italian from dictation. Beside the annual examination at the close of the Second Term, the Sophomores attended three written examinations.
Instruction was given in Spanish as follows : —
To a section of the Senior Class, which attended three recitations a week, and read Moratin’s “El sí de las niñas,” Lope de Vega’s “La Estrella de Sevilla,” and portions of “Don Quijote.” This section wrote Spanish from dictation, and also translations from English into Spanish. They had one private examination in writing, beside the Annual Examination at the close of the Second Term.
To a section of the Junior Class, which recited twice a week, studying Josse’s Grammar and Reader, and portions of Le Sage’s “Gil Blas.”
- LATIN.
During the last year this Department was under the superintendence of George M. Lane, Ph. D., University Professor of Latin, aided by Mr. James B. Greenough and Mr. Prentiss Cummings, Tutors. The instruction of the Senior and Junior Classes was conducted by Professor Lane, that of the Sophomore Class by Mr. Cummings, and that of the Freshman Class by Mr. Greenough.
Instruction was given to the Freshman Class in Lincoln’s Selections from Livy (two Books), the Odes of Horace, Cicero’s Cato Major, Roman Antiquities, and in writing Latin:
To the Sophomore Class, in Cicero’s Laelius, Cato Major, and Select Epistles; Terence’s Phormio, Eunuchus, and Adelphi; Quintus Curtius, selections from Ovid, Seneca’s Hercules Furens, and in Writing Latin:
To the Junior Class, in Horace’s Satires, Tacitus’s Annals, and Juvenal :
To the Seniors, in Juvenal, Cicero de Deorum Natura, Lucretius, and Plautus, in the regular elective division. Besides this, instruction was given to the candidates for Honors, in Tacitus and in Latin Composition.
- GREEK.
The Greek Department, in the absence of William W. Goodwin, Ph. D., Eliot Professor of Greek Literature, was under the charge of Evangelinus A. Sophocles, LL.D., University Professor of Ancient, Byzantine, and Modern Greek, and Isaac Flagg, A. M., and William H. Appleton, A.M., Tutors in Greek.
The Freshmen were instructed by Mr. Flagg and Mr. Appleton. They were divided into four sections, and attended four recitations a week during each Term, besides exercises in Greek Composition. The text-books were Xenophon’s Memorabilia, the Odyssey, and Lysias.
The Sophomores were instructed by Mr. Flagg. They recited twice a week, in four sections, and read the Prometheus of Aeschylus, the Birds of Aristophanes, and the Olynthiacs of Demosthenes. The elective section in advanced Greek read also Plato’s Apology and Crito, the Alcestis of Euripides, and half of the First Book of Herodotus. The Class was also instructed in Greek Composition.
An elective section of Juniors read the first three books of Polybius with Professor Sophocles. A section of Juniors read Aeschines, and Demosthenes on the Crown with Mr. Flagg.
An elective section of Seniors read Plato’s Apology and Crito, and the Electra of Sophocles with Mr. Flagg; and another section read the Antigone of Sophocles, the Alcestis of Euripides, and Thucydides with Professor Sophocles.
- HEBREW.
This Department, vacant the First Term, was filled the Second Term by Rev. Edward J. Young, Hancock Professor of Hebrew and other Oriental Languages, who gives instruction twice a week to such students as desire it.
- NATURAL HISTORY.
This Department, now wholly elective, was, in the absence of Professor Gray, under the care of Wm. T. Brigham, A.M.
The course was attended by sixty-four Students of the Junior Class; and the instruction was given by recitations in Structural Botany, lectures on Vegetable Physiology and Organography, and practical work in plant-analysis with the microscope, followed by oral and written examinations. Each student was occupied three hours each week in the lecture-room. From the Thanksgiving recess to the end of the First Term the Class attended recitations and lectures on Animal Physiology and Anatomy, under the care of Jeffri9es Wyman, M. D.
- ANATOMY AND PHYSIOLOGY.
A course of twenty Lectures on the Anatomy and Physiology of Vertebrated Animals was delivered during the First Term, to members of the Senior Class, and to members of the Professional Schools, by Jeffries Wyman, M.D., Hersey Professor of Anatomy. The Lectures were given on Tuesdays and Thursdays, at 12 M. During the second half of the First Term, fifty members of the Junior Glass attended recitations from a text-book on Physiology, on Wednesdays and Fridays, from 10 to 12 A.M.
- CHEMISTRY AND MINERALOGY.
The instruction in this Department was given by Josiah P. Cooke, A.M., Erving Professor, and George A. Hill, A.B., Tutor in Physics and Chemistry. During the First Term the Sophomore Class studied Cooke’s Chemical Physics, reciting in three divisions twice each week, and passing two private examinations during the Term. In the Second Term the same Class studied “The First Principles of Chemical Philosophy,” passing one private examination, and the usual public examination at the end of the year. They also attended a course of Lectures, one each week, on General Chemistry.
Those of the Junior Class who elected this department attended during the whole year a course of instruction in Practical Chemistry, giving their attendance in the Laboratory six hours each week, in addition to the three regular hours of recitation. The text-books used were Galloway’s Qualitative Chemical Analysis and Cooke’s Chemical Philosophy; but the course is specially designed to train the faculties of observation and to teach the methods of scientific study, and hence the greater part of the instruction is necessarily oral. The course of Lectures on General Chemistry begun in the Second Term of the Sophomore was continued during the First Term of the Junior Year, two each week until the end of the Term.
Those of the Senior Class who elected Chemical Physics received instruction in Crystallography during the First Term (the text-book used being Cooke’s Chemical Physics), and during the Second Term in Blowpipe Analysis and in Mineralogy, the course consisting of Lectures and practical instruction in the laboratory and cabinet. Elderhorst’s Blowpipe Analysis and Dana’s Manual of Mineralogy were used as books of reference.
- PHYSICS.
During the last academic year instruction in this Department was conducted by George A. Hill, A.B., Tutor in Chemistry and Physics. Joseph Lovering, A.M., Hollis Professor of Mathematics and Natural Philosophy, was absent in Europe through the year, so that the usual courses of Lectures on Physics to the Senior and Junior Classes were not given.
The whole Junior Class recited to Mr. Hill three times a week during the First and Second Terms; and read Herschel’s Outlines of Astronomy and Lardner’s Course of Natural Philosophy [Optics]. This Class was examined at the end of the Second Term in both books.
The Class recited in three Divisions; each Division remaining with the instructor one hour at every exercise; in all nine hours a week.
- MATHEMATICS.
The instruction in this Department was given by Benjamin Peirce, LL.D., Perkins Professor of Astronomy and Mathematics; James Mills Peirce, A.M., Assistant Professor of Mathematics; Edwin P. Seaver, A.M., Tutor; and George V. Leverett, A.B., Instructor.
The Freshman Class recited, throughout the year, in four sections three times in the week, and in two sections, once in the week, from the following text-books: Peirce’s Plane and Solid Geometry, and Peirce’s Algebra. The Freshmen were also instructed in Plane Trigonometry.
The study of Mathematics was elective during the Sophomore, Junior, and Senior years.
In the Sophomore year the instruction in Pure and Applied Mathematics was arranged in four courses of two lessons a week each, and Students were allowed to elect one or more of these courses. The subjects taught were Analytic Geometry (Puckle’s Conic Sections, and lectures on the Elements of Analytic Geometry of Three Dimensions), the Differential Calculus (lectures and examples), Spherical Trigonometry
(lectures and examples), Elementary Mechanics (Goodwin and Kerr), and the Theory of Sound (Peirce).
Instruction was given to those who elected Mathematics in the Junior and Senior years, by lectures and recitations, on three days in the week, throughout the year, in Differential, Imaginary, Integral, and Residual Calculus, in the Calculus of Quaternions, and in the Mathematical Theory of Mechanics and Astronomy.
Applied Mathematics (Kerr’s Elementary Mechanics) was also an elective study in the Junior year.
[…]
COURSE OF INSTRUCTION FOR THE ACADEMICAL YEAR, 1868-69.
[…]
SENIOR CLASS.
FIRST TERM.
- Philosophy. Bowen’s Ethics and Metaphysics.—Bowen’s Political Economy.—Forensics.
- Modern History. Guizot’s and Arnold’s Lectures.—Story’s Abridged Commentaries on the Constitution.
ELECTIVE AND EXTRA STUDIES.
- Philosophy. Mill’s Examination of Hamilton’s Philosophy.—Last 140 pages of Bowen’s Logic.
- Mathematics. Peirce’s Analytic Mechanics.
- History. May’s Constitutional History.—Mill on Representative Government.
- Chemistry. Crystallography and Physics of Crystals.
- Greek. The Antigone of Sophocles.—The Alcestis of Euripides.
- Latin. Juvenal.—Cicero de Deorum Natura.—Tacitus’s Annals and Latin Exercises, with an extra Division.
- German. Goethe’s Egmont.—Schiller’s Wallenstein’s Lager und Maria Stuart.—Exercises in Writing German.
- French. Mennechet’s Littérature Française Classique.—La Fontaine’s Fables.—Writing French.
- Advanced Spanish. Moratin’s El sí de las niñas.—Lope de Vega’s La Estrella di Sevilla.
- Advanced Section. Tasso’s Gerusalemme.
- English. Thorpe’s Analecta Anglo-Saxonica.—Mätzner’s Alt-englische Sprachproben.
- Modern Literature. Lectures.
- Patristic and Modern Greek.
- Geology. Lectures.
- Anatomy. Lectures.
SECOND TERM.
- History. Hallam’s Middle Ages, one volume.
- Religious Instruction.
- Political Economy. Bowen’s, finished.
- Rhetoric. Themes.
ELECTIVE AND EXTRA STUDIES.
- Philosophy. Schwegler’s History of Philosophy (Selections).—Mansel’s Limits of Religious Thought.—Exercises and Lectures.
- Mathematics. Peirce’s Analytic Mechanics.—Lectures on Quaternions.
- Greek. Thucydides, First two Books.—Homer’s Iliad, Book IV.
- Latin. Lucretius and Plautus (Selections).
- History. Constitutional History.—Constitution of the United States, and the Federalist.
- Chemistry. Mineralogy and Determination of Minerals.
- German. Die Braune Erika.—Goethe’s Hermann and Dorothea.—Faust.—Writing German.
- French. Mennechet’s Littérature Française Classique.—Molière’s Misanthrope.—Beaumarchais’s Barbier.—Lessons in French Pronunciation.
- Advanced Spanish. Don Quijote.
- Advanced Section. Dante’s Divina Commedia.
- English. Studies of First Term continued.
- Zoölogy. Lectures.
- Modern Literature. Lectures.
- Patristic and Modern Greek.
[…]
The required studies of the Senior Class are History, Philosophy, and Ethics (together five hours a week). The elective studies are Greek, Latin, Mathematics, Physics, Chemical Physics, History, Philosophy, and Modern Languages (French, German, Italian, and Spanish). In each elective department there will be three exercises a week. Each Senior may choose three or two electives (at his pleasure), and receive marks for the same. Special students for honors may be permitted to devote the whole nine hours to two elective departments, under such restrictions as may be prescribed. Marks will be allowed in Modern Languages in the Senior year to advanced students only.
Source: Harvard University. Annual Reports of the President and Treasurer of Harvard College, 1868-69.
Image Source: Portrait of Francis Bowen from the Harvard Square Library (Unitarian Universalism). The Harvard Book: Portraits.
means that “investment decisions are always carried out”, so that when
and interpret and analyze the resulting model. Compare its behavior with the case analyzed in class.
where m is the real per capita stock of money, k is the capital-labor ratio, and 
is the expected rate of inflation which is equal to the actual rate 
in the steady state.
is the rate of inflation in (b) that maximizes steady state consumption per head. Would a higher rate of inflation lead to a higher or lower long-run capital-labor ratio?![\dot{k}=sf\left( k \right)-nk-\left( 1-s \right)\left[ \dot{m}+nm+{{\pi }_{m}}m \right]{{p}_{m}}](https://s0.wp.com/latex.php?latex=%5Cdot%7Bk%7D%3Dsf%5Cleft%28+k+%5Cright%29-nk-%5Cleft%28+1-s+%5Cright%29%5Cleft%5B+%5Cdot%7Bm%7D%2Bnm%2B%7B%7B%5Cpi+%7D_%7Bm%7D%7Dm+%5Cright%5D%7B%7Bp%7D_%7Bm%7D%7D&bg=ffffff&fg=000&s=0&c=20201002)
![{{p}_{m}}m=L\left[ {{p}_{m}}m+k,{{\pi }_{m}},{f}'\left( k \right),f\left( k \right) \right]](https://s0.wp.com/latex.php?latex=%7B%7Bp%7D_%7Bm%7D%7Dm%3DL%5Cleft%5B+%7B%7Bp%7D_%7Bm%7D%7Dm%2Bk%2C%7B%7B%5Cpi+%7D_%7Bm%7D%7D%2C%7Bf%7D%27%5Cleft%28+k+%5Cright%29%2Cf%5Cleft%28+k+%5Cright%29+%5Cright%5D&bg=ffffff&fg=000&s=0&c=20201002)
, that is that the government always vary its deficit to produce a constant rate of deflation 
(which would, of course, be an inflation if .) 
![\dot{k}=\frac{sf\left( k \right)-nk-\left( 1-s \right)n\left( {{p}_{m}}m \right)}{\left[ 1+\left( 1-s \right)C \right]}](https://s0.wp.com/latex.php?latex=%5Cdot%7Bk%7D%3D%5Cfrac%7Bsf%5Cleft%28+k+%5Cright%29-nk-%5Cleft%28+1-s+%5Cright%29n%5Cleft%28+%7B%7Bp%7D_%7Bm%7D%7Dm+%5Cright%29%7D%7B%5Cleft%5B+1%2B%5Cleft%28+1-s+%5Cright%29C+%5Cright%5D%7D&bg=ffffff&fg=000&s=0&c=20201002)
![C={\left[ {{L}_{1}}+{{L}_{3}}{f}''+{{L}_{4}}{f}' \right]}/{\left( 1-{{L}_{1}} \right)}\;>0](https://s0.wp.com/latex.php?latex=C%3D%7B%5Cleft%5B+%7B%7BL%7D_%7B1%7D%7D%2B%7B%7BL%7D_%7B3%7D%7D%7Bf%7D%27%27%2B%7B%7BL%7D_%7B4%7D%7D%7Bf%7D%27+%5Cright%5D%7D%2F%7B%5Cleft%28+1-%7B%7BL%7D_%7B1%7D%7D+%5Cright%29%7D%5C%3B%3E0&bg=ffffff&fg=000&s=0&c=20201002)
the same regardless of 
on the stable steady-state stock of capital?
