9.7 Consider a generalisation of the production function in Example 9.3: q = 0 + 1!kl + 2k + 3l , where 0 i

9.7 Consider a generalisation of the production function in Example 9.3:

q = β0 + β1!kl + β2k + β3l , where 0 ≤ βi ≤ 1, i = 0,…, 3.

a. If this function is to exhibit constant returns to scale, what restrictions should be placed on the parameters β0, … , β3?

b. Show that, in the constant returns-to-scale case, this function exhibits diminishing marginal productivities and that the marginal productivity functions are homogeneous of degree 0.

c. Calculate s in this case. Although σ is not in general constant, for what values of the β’s does s = 0, 1, or ∞?