Microeconomics
2nd Edition
ISBN: 9781259813337
Author: KARLAN, Dean S., Morduch, Jonathan
Publisher: Mcgraw-hill Education,
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Chapter A, Problem 6PA
To determine
Creation of graph with
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Problem 2. If the consumer preference can be represented by a CES function with δ = 0.5, i.e. u(x, y) = x0.5 + y0.5. Let the prices and income be (px, py, w).
1. Set up the Lagrangian expression.2. Take the first-order conditions.3. Substitute into budget constraint to derive the optimal consumption bundles.
1. A town relies on four different sources for its non-drinking water needs: dam water,
reclaimed water, rain water, and desalinated water. The different sources carry different
risks and costs. For instance, desalinated water is fully reliable due to abundant sea water,
but it is more expensive than other options. Reclaimed water also has relatively lower
risk than rain or dam water since a certain amount can be obtained, even during the dry.
season, by the treatment of daily generated waste water.
Using any of the four options requires an investment in that resource. The return on a
particular water source is defined as the amount of water generated by the source per
dollar of investment in it. The expected returns and standard deviations of those returns
for the four water sources are described in the following table:
Water resource
Expected return St. Deviation
Dam water
2.7481
0.2732
Reclaimed water
1.6005
0.0330
Rain water
0.5477
0.2865
Desalinated water
0.3277
0.0000
Higher…
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