(a) For the cost function C(w₁, W2, y) 2y ww, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (ri(w₁, W2, y), x(w₁, W2, y)). = (b) Consider the production function f(x, y, z) = √ry+xz+yz. Find the scale elasticity SE at (x, y, z) = (1, 2, 3), (5, 1, 6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer

(a) For the cost function C(w₁, W2, y) 2y ww, calculate the Allen elasticity of substitution between the two inputs at the cost-minimizing input point (ri(w₁, W2, y), x(w₁, W2, y)). = (b) Consider the production function f(x, y, z) = √ry+xz+yz. Find the scale elasticity SE at (x, y, z) = (1, 2, 3), (5, 1, 6), (6, 6, 6) and determine if the pro- duction function is IRTS, CRTS, or DRTS locally at each point. (c) A profit maximizing firm in the market operates where the production exhibits decreasing return to scale (DRTS). Is this market in its long-run equilibrium? Justify your answer

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

(a) For the cost function C(w1, w2, y) = 2y²w} w, calculate the Allen elasticity
of substitution between the two inputs at the cost-minimizing input point
(xf(w1, w2, y), a(w1, w2, y)).
(b) Consider the production function f(r, y, z) = Vry + rz+ yz. Find the scale
elasticity SE at (x, y, z) = (1,2, 3), (5, 1,6), (6, 6, 6) and determine if the pro-
duction function is IRTS, CRTS, or DRTS locally at each point.
(c) A profit maximizing firm in the market operates where the production exhibits
decreasing return to scale (DRTS). Is this market in its long-run equilibrium?
Justify your answer.
(d) Suppose that there are the infinite number of potential firms that produce the
identical output good y under the cost function C(y) = + 3. Assume free
entry and exit. Find the long-run equilibrium output price p, the amount of
the output that each firm in the market produces in the long-run equilibrium,
and the value of profit that each firm earns in the equilibrium.

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Step 1: Introduction

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Step 2: (a) Allen Elasticity of Substitution

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Step 3: Marginal rate of technical substitution

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Step 4: (b) Scale Elasticity at Various Points

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Step 5: (c) Market Equilibrium with DRTS Production

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Subpart 1-3
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