Consider a Cobb-Douglas production function f: ℝ²₊ → ℝ₊, given by f(z) = 2¾z₁ⁱ⁴z₂ⁱ⁴, where z ≫ 0 denotes inputs in the production process.
(1) Does the production function exhibit non-increasing, non-decreasing, or constant returns to scale? Explain.
(2) Derive the supply function and the profit function, and verify properties (a) and (d) of Proposition 12.4. (The supply correspondence (function) is homogeneous of degree zero, and the profit function is homogeneous of degree one.)