Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α

(a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing.

(b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?

(c) For what values of α are the isoquants of q(k, l) convex?

(d) Show that this function is homogeneous of degree one.

(e) Show that the marginal product functions are homogeneous of degree zero.

(f) Show that the production function exhibits constant returns to scale.

Expert Solution

Kindly refer to the images attached (in order) for the solution to your question:

Note that the answers to the second part of sub-part (b) and part (c) is the same and hence have been clubbed together.

Rahul Sunny answered 2 years ago

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