There are only marginal differences to be found from the course outline for 1941-42 and 1942-43, e.g. “Time lags and sequences” instead of “Cobweb Model” plus addition of Mosak (General Equilbrium Theory in International Trade) and Samuelson (Foundations of Economic Analysis) to the course bibliography. We also see that Marshall’s Mathematical Appendix was a “new” assignment for the reading period. Midterm and Final exam questions are included in this posting.
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[Course Outline, Leontief]
Economics 4a
Spring Term, 1948
Introduction to the Mathematical Treatment of Economic Theory
- Introductory remarks
Profit function
Maximizing profits - Cost functions: Total costs, fixed costs, variable costs, average costs, marginal costs, increasing and decreasing marginal costs.
Minimizing average total and average variable costs - Revenue function
Price and marginal revenue
Demand function
Elasticity and flexibility - Maximizing the net revenue (profits)
Monopolistic maximum
Competitive maximum
Supply function - Joint costs and accounting methods of cost imputation
Multiple plants
Price discrimination - Production function
Marginal productivity
Increasing and decreasing productivity
Homogeneous and non-homogeneous production functions - Maximizing net revenue, second method
Minimizing costs for a fixed output
Marginal costs and marginal productivity - Introduction to the theory of consumers’ behavior
Indifference curves and the utility function - Introduction to the theory of the market
Concept of market equilibrium
Duopoly, bilateral monopoly
Pure competition - Time lag and time sequences
- Introduction into the theory of general equilibrium
Bibliography:
R. G. D. Allen, Mathematical Analysis for Economists
Evans, Introduction into Mathematical Economics
Antoine Cournot, Researches into the Mathematical Principles of the Theory of Wealth
Jacob L. Mosak, General Equilibrium Theory in International Trade
Paul A. Samuelson, Foundations of Economic Analysis
Reading Period Assignment: Alfred Marshall, Principles of Economics, Mathematical Appendix
Source: Harvard University Archives. Syllabi, course outlines and reading lists in Economics, 1895-2003. HUC 8522.2.1, Box 4, Folders “Economics, 1947-1948 (1 of 2)”. Copy also in Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.
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[Midterm Exam]
Economics 4a
Hour Examination
March 23, 1948
Answer two questions, including Question 3.
1. Prove that the average costs tend either
(a) toward equality with the marginal costs, or
(b) toward infinity
as the output of an enterprise is reduced toward zero.
2. Describe the relationship between the cost curve and the supply curve of an enterprise.
3. An industrial enterprise produces jointly two kinds of outputs, X and Y and uses one kind of input, Z. Given
(a) the production function z = f(x,y), where z, x and y are quantities of Z, X and Y and
(b) the prices Pz, Px and Py of Z, X, and Y
derive the equations the solution of which would determine the most profitable input-output combination. Don’t forget the secondary conditions.
Source: Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.
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[Final Exam]
1947-48
HARVARD UNIVERSITY
ECONOMICS 4a
Please write legibly
Answer four questions including question 6.
- Show how a change in the magnitude of the fixed costs would affect the supply curve of a profit-maximizing enterprise selling its product on a competitive market.
- Given:
The production function,
x = yz2
where x is the quantity of output, and y and z represent the amounts of two different inputs purchased at the fixed prices py and pz respectively,
Derive:
The total cost curve of the enterprise. (A total cost curve represents the functional relationship between various outputs and the smallest total costs at which they can be produced.)
- A monopolistic producer sells his output in two separate markets. His cost curve is:
C = K + Q
where C represents the total cost, Q the total output, and K a positive constant. The demand curves in the two markets are:
p1 = A – q1
p2 = B – q2,
p1, p2 and q1, q2 represent the prices charged and quantities demanded in the two markets respectively. A and B are positive constants.
What prices would the monopolist charge in the two markets in order to maximize his total net revenue?
- A worker maximizes his utility function:
u(c, l)
where c represents his consumption and l the number of hours worked. The hourly wage rate is w dollars.
Determine the equation showing how many hours of labor, l, the worker will supply at any given wage rate, w. Analyze the conditions under which an increase in the wage rate might reduce the number of hours worked.
- Discuss the problem of measurability of utility.
- A consumer receives a fixed income y1 in “year I” and a fixed income y2 in “year II.” He is free to augment his consumption during year I by borrowing money from the outside on condition that it be paid back with interest out of the income of year II. He can also spend during the first year less than his total income y1. The resulting savings plus the accrued interest will be added in this case to the second year’s consumption. No transfer of any savings beyond the second year and no borrowing against the income of the later years is allowed.
Given:
(a) the utility function,
u(x1, x2)
to be maximized where x1 and x2 stand for the consumption of the first and the second year, and
(b) the rate of interest i
Derive:
(1) the equations which determine the optimum amount of savings (or borrowings) s;
(2) the formula showing the effect of an infinitesimal change in the rate of interest i on the amount of savings (or borrowings) Interpret the meaning of such a formula.
Final. May, 1948.
Source: Harvard University Archives, Wassily Leontief Papers. Course Material Box 2 (HUG 4517.45); Folder “Spring 1948-Econ. 4A”.
Image Source: Harvard Album, 1947.