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PaulKet PaulKet
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6 years ago
A consumer has preferences given by the constant elasticity of substitution utility function:
      U(q1,q2) = (q1.5 + q2.5)2
a.   Write the Lagrangian for the consumer's maximization problem.
b.   Use the Lagrangian to solve for the optimal quantities in terms of the prices and income.
Textbook 
Microeconomics: Theory and Applications with Calculus

Microeconomics: Theory and Applications with Calculus


Edition: 4th
Author:
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The curious task of economics is to demonstrate to men how little they really know about what they imagine they can design.

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#1
6 years ago
a.   L = (q1.5 + q2.5)2 + [Y - p1q1 - p2q2]
b.   The first-order conditions are
   dL/dq1 = 2(q1.5 + q2.5).5q1-.5 - p1 = 0
   dL/dq2 = 2(q1.5 + q2.5).5q2-.5 - p2 = 0
   dL/dl = Y - p1q1 - p2q2 = 0
   The first two conditions yield:
      q2/q1 = (p1/p2)2
   Substitute into the third condition (i.e. the budget constraint):
      Y = p1q1 + p2(p1/p2)2q1
   Solve for q1:
      q1 = Y/(p1 + p1/p22)
      q2 = Y/(p2 + p2/p12)
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