A consumer has utility function U(21, 2) =4 +8 where z and zz are the two goods. Market prices are given by p (PL.P2) and the consumer's income is given by y. Ex. 1 • Set up the utility maximization problem and derive the Walrasian demand for the two goods. • Compute the elasticity of the demand for good z2 with respect to income y. Which kind of good is good z2? Compute the indirect utility function v(p; y) and verify its main properties.
A consumer has utility function U(21, 2) =4 +8 where z and zz are the two goods. Market prices are given by p (PL.P2) and the consumer's income is given by y. Ex. 1 • Set up the utility maximization problem and derive the Walrasian demand for the two goods. • Compute the elasticity of the demand for good z2 with respect to income y. Which kind of good is good z2? Compute the indirect utility function v(p; y) and verify its main properties.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.12P
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Transcribed Image Text:Ex. 1
two goods. Market prices are given by p (PL.P2) and the consumer's income is given by y.
A consumer has utility function U(11, 12) = 1*2 + 8 where zį and r2 are the
Set up the utility maximization problem and derive the Walrasian demand for the two goods.
• Compute the elasticity of the demand for good r2 with respect to income y. Which kind of good
is good z2?
Compute the indirect utility function v(P: ) and verify its main properties.
Ex. 2
A firm produces output Z combining input X and Y according to the following
technology:
Z = f (X,Y) = K (aX² + (1-a) Y)
The cost of input X is wx, while the cost of input Y is wy. The price of output Z is p. The firm is
price-taker both on the input markets and on the output market.
Compute the conditional input demand function.
Compute the elasticity of substitution. Interpret this quantity.
• Compute the cost function. How does the cost function marginally change if you modify the
price of one input? Explain.
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