Question

(2) Given that the production function for a firm is: $\Phi(z) = [\alpha_1 z_1^{-1} + \alpha_2 z_2^{-1} + \alpha_3 z_3^{-1} + \alpha_4 z_4^{-1}]^{-1}$ where $z_i$ denotes production input $i$ and $\alpha_i$ denotes a parameter for $i = 1, \dots, 4$. (a) Sketch the long-run marginal and average cost curves and briefly comment on their form. (b) If input 3 and input 4 are both fixed in the short-run then derive the short-run cost function as well as the short-run marginal and average cost functions and briefly comment on them. (c) Derive the short-run supply function for the firm and briefly comment on it. (d) Calculate the short-run elasticity of supply for the firm and briefly comment on it.

          (2)
Given that the production function for a firm is:
$\Phi(z) = [\alpha_1 z_1^{-1} + \alpha_2 z_2^{-1} + \alpha_3 z_3^{-1} + \alpha_4 z_4^{-1}]^{-1}$
where $z_i$ denotes production input $i$ and $\alpha_i$ denotes a parameter for $i = 1, \dots, 4$.
(a) Sketch the long-run marginal and average cost curves and briefly comment on their form.
(b) If input 3 and input 4 are both fixed in the short-run then derive the short-run cost function as well
as the short-run marginal and average cost functions and briefly comment on them.
(c) Derive the short-run supply function for the firm and briefly comment on it.
(d) Calculate the short-run elasticity of supply for the firm and briefly comment on it.

(2)
Given that the production function for a firm is:
Φ(z) = [α1 z1^-1 + α2 z2^-1 + α3 z3^-1 + α4 z4^-1]^-1
where zi denotes production input i and denotes a parameter for i = 1, …, 4.
(a) Sketch the long-run marginal and average cost curves and briefly comment on their form.
(b) If input 3 and input 4 are both fixed in the short-run then derive the short-run cost function as well
as the short-run marginal and average cost functions and briefly comment on them.
(c) Derive the short-run supply function for the firm and briefly comment on it.
(d) Calculate the short-run elasticity of supply for the firm and briefly comment on it.

Added by Sandra B.

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