Question

1. Sketch the production isoquant for a production function that takes two inputs (e.g. y = f[l,k]). Show the cost minimizing combination of inputs by adding an isocost line to your sketch.
(a) What is the relationship between the trs and the relative price of one input compared to the other at the cost minimizing combination of inputs?

(b) What does the assumption of a diminishing technical rate of substitution (trs) mean? (What does a diminishing trs mean imply for a firm’s willingness to pay for one input compared to another?)

2.  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) Assuming the wage is low (i.e. the firm can save money by using technique 1), add the isocost curve that would represent the least-cost means of producing the good to your sketch.

(c) Is there a price at which the firm is ambivalent as to which techniques to use? If so, 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?

Answer 1

Capital & Labor

a. In the diagram, AB represents iso cost line and IQ1 is the isoquant representing the level of output produced by the economy. As the diagram clearly shows that the cost minimizing level of output occurs at point E1 where the slope of isoquant which is equal to technical rate of substitution is equal to the slope of iso cost lone which is the relative input price ratio. Thus, at the cost minimizing combination of inputs, TRS and relative price of one input compared to the price of another input are same.

b. The assumption of diminishing marginal technical rate of substitution means the rate at which one factor must decrease so that same level of productivity can be maintained when another factor is increased.