03 May WHAT DOES THE ASSUMPTION OF DIMINISHING MARGINAL PRODUCTIVITY IMPLY FOR THE SHAPE OF THE PRODUCTION SET?
Intermediate Microeconomics (ECON 2020)
Problem Set # 3
Markus P. A. Schneider
October 13, 2016
Answer each question completely (all parts) and indicate your final answer clearly. It is important that you
show all the steps in your reasoning to receive full credit for your answer.
1. Define the following terms as rigorously as you can.
(a) Marginal Product (of a factor of production)
(b) Opportunity Cost
(c) Technical Rate of Substitution
2. Answer the following questions about a firms production set.
(a) How many different production techniques are are represented by a production set with
a smoothly curved boundary?
(b) What does the assumption of diminishing marginal productivity imply for the shape of
the production set? Provide a sketch to illustrate your answer. What does this mean
for the returns to scale?
(c) Given the general sketch of a cost curve (e.g., what you used on Problem Set #2),
comment on whether the firm faces decreasing-, constant-, and increasing returns to
scale, or all of the above. Sketch a production set that would be consistent with this
general cost curve.
(d) Is the production set you sketched in (c) convex?
3. What does the assumption of a diminishing technical rate of substitution (TRS) mean? How
is the TRS related to the price of one input compared to that of another? What does
a diminishing TRS mean imply for a firms willingness to pay for one input compared to
another?
1
4. Sketch the production isoquants for each of the following types of production functions assum-
ing there are two inputs and one output. Also state whether the given production functions
implies that one input can be substituted for the other.
(a) Fixed Factor (Fixed Proportions)
(b) Cobb-Douglas
5. A firm can choose between two techniques to produce a good, each of which relies on labor, l,
and capital, k, in fixed proportions (fixed factor production). Technique 1 uses more labor and
requires only a minimal investment in machinery, while technique 2 is more capital-intensive
but requires little labor. Use this information to answer the following questions.
(a) Sketch the production isoquants for each technique (assume both produce the same level
of output).
(b) Assume the price of labor is low so that the firm can save money by using technique
1. Add a isocost curve to your sketch that would represent the least-cost means of
producing the good. How is the price of labor relative to capital represented on your
sketch?
(c) Is there a price at which the firm is ambivalent as to which techniques to use? Add the
corresponding isocost curve to your sketch. What happens if the price of labor increases
beyond the price at which the firm might use either technique?
6. In a entry on the Harvard Business Review blog, Jonathan Schlefer 1 noted that “in 2006,
when Ford opened a plant in Chongqing, China, where wages were a fraction of the German
level, a spokesman said it was ‘practically identical to one of its most advanced factories in
Germany.” Answer the following questions related to this observation.
(a) Is this observation consistent with the assumption of substitutability embodied in the
Cobb-Douglas production function for the firm?
(b) Read the last example at the very end of chapter 19 in Varian (“Copy Exactly!”). What
might be some reasons not covered by the model of technology in chapter 19 why Ford
decided not to opt for a different production technique when it opened its plant in China?
(c) How realistic do you think it is to assume a smooth production function with diminishing
TRS for all firms and at all scales of production? If you think it is an unrealistic
assumption in general, what would that imply about the idea that “factors are paid
according to their marginal product”?
1 Dr. Schlefer is a political scientist with a PhD from MIT and a research associate at the Harvard Business School
(h
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