# Production Theory Functions

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Question

Consider a firm with production function .

(a) Sketch the isoquant diagram of this firm.

(b) Derive the marginal rate of technical substitution between the two inputs. What is the relationship between the marginal rate of technical substitution and the isoquants drawn in subquestion (a).

(c) Does the function exhibit decreasing, constant, or increasing returns to scale? Is homogeneous of some degree k>0?

(d) Write down the firm's cost minimization problem.

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#### Solution Preview

Please see the attached file.

Question: Consider a firm with production function

(a) Sketch the isoquant diagram of this firm.

For f = 1, = 1, or 3 = 1 - , or z2 =

For f = 2, = 2, or 3 = 2 - , or z2 =

For f = 3, = 3, or 3 = 3 - , or z2 =

For f = 4, = 4, or 3 = 4 - , or z2 =

(b) Derive the marginal rate of technical substitution between the two inputs. What is ...

#### Solution Summary

The expert examines a firm with production functions. The Isoquant diagram of the firm are sketched.