Technical Rate of Substitution (TRS)

1. Define the following terms as rigorously as you can.

(a) Increasing Returns to Scale
(b) Marginal Product (of a factor of production)
(c) Opportunity Cost

2. What is the Technical Rate of Substitution (TRS)? What does convexity of the ?rm’s pro-
duction set imply about the TRS? How is the TRS related to the price of one input compared
to another (i.e. the relative price of the input)? Answer each question in your own words.

3. 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 Proportions
(b) Perfect Substitutes
(c) Cobb-Douglas

4. A ?rm can choose between two techniques to produce a good, each of which relies on labor, l,
and capital, k in ?xed proportions. Technique 1 uses more labor and requires only a minimal
investment in machinery, while technique 2 is much 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 ?rm 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 ?rm should switch between techniques? Add the corre-
sponding isocost curve to your sketch.

1
5. In a entry on the Harvard Business Review blog, Jonathan Schlefer1 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 ?rm?
(b) Read the last example at the very end of chapter 18 in Varian (“Copy Exactly!”). What
might be some reasons not covered by the model of technology covered in chapter 18
why Ford decided not to opt for a di?erent 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 ?rms? 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”?

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