Chapter 5: Production
Production Theory
Chapter Review
The production function defines the relationship among various inputs and the maximum
quantity of a good that can be produced. Managers study production functions to gain insights
into the firm's cost structure.
An isoquant is a curve showing all possible (efficient) combinations of inputs capable of
producing a particular quantity of output. The marginal rate of technical substitution shows the
rate at which one input can be substituted for another input if output were held constant. No
profit-maximizing manager will operate at a point where the isoquant is positively sloped.
To minimize the cost of producing a particular output, a manager should allocate expenditures
among various inputs so that the ratio of the marginal product to the input price is the same for
all inputs used. Graphically, this amounts to choosing the input combination where the relevant
isoquant is tangent to an isocost curve.
If a manager increases all inputs by the same proportion and output increases by more (less)
than this proportion, there are increasing (decreasing) returns to scale. Increasing returns to
scale may occur because of indivisibility of inputs, various geometrical relations, or
specialization. Decreasing returns to scale can also occur; the most frequently cited reason is the
difficulty of managing a huge enterprise. Whether there are constant, increasing, or decreasing
returns to scale is an empirical question that must be settled case by case. Managers have
estimated production functions in many firms and industries. Many studies show that a Cobb-
Douglas function is the best fit for the data.
1 If the production function is the same as is given in question 17, which of the following is a
true statement regarding the marginal product of capital?
1. It is smaller than the marginal product of labor.
2. It is decreasing with respect to labor.
3. It is increasing with respect to capital.
4. It satisfies the property of diminishing marginal returns.
5. None of the given choices are correct.
2 The marginal rate of technical substitution equals minus one times the slope of the isoquant.
