9.8 0 i 1, i = 0,, 3. If this function is to exhibit constant returns to scale, what restrictions should be placed

9.8 0 ≤ βi ≤ 1, i = 0,…, 3.

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

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.

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

Show that Euler’s theorem implies that, for a constant returns-to-scale production function [q = f (k, l )], q = fk

· k + fl

· l

.

Use this result to show that, for such a production function, if MPl > APl then MPk must be negative. What does this imply about where production must take place? Can a firm ever produce at a point where APl is increasing?