This questions examines the Lump Sum Principle on subsidies. Consider an indi- vidual with a Cobb-Douglas utility function U(x, y) = x¹/²y¹/2, and faces prices Pa, Py with an income of $1. (a) First, find the optimal demand for x and y and compute the indirect utility function, V(P, Py, I). (b) Now let pr = 1 and Py = 4. Use the expenditure function E(pa, Py, U), to calculate the extra income needed to increase the individual's utility from U = 2 to U = 3. (c) Now estimate the degree to which good x must be subsidized to increase this person's utility from U = 2 to U = 3. How much would this subsidy cost the
This questions examines the Lump Sum Principle on subsidies. Consider an indi- vidual with a Cobb-Douglas utility function U(x, y) = x¹/²y¹/2, and faces prices Pa, Py with an income of $1. (a) First, find the optimal demand for x and y and compute the indirect utility function, V(P, Py, I). (b) Now let pr = 1 and Py = 4. Use the expenditure function E(pa, Py, U), to calculate the extra income needed to increase the individual's utility from U = 2 to U = 3. (c) Now estimate the degree to which good x must be subsidized to increase this person's utility from U = 2 to U = 3. How much would this subsidy cost the
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1*. This questions examines the Lump Sum Principle on subsidies. Consider an indi-
vidual with a Cobb-Douglas utility function U(x, y) = x¹/2y¹/2, and faces prices Pa, Py
with an income of $1.
(a) First, find the optimal demand for x and y and compute the indirect utility
function, V(P, Py, I).
(b) Now let p
=
: 1 and py = 4. Use the expenditure function E(pa, py, U), to calculate
the extra income needed to increase the individual's utility from U = 2 to U = 3.
(c) Now estimate the degree to which good x must be subsidized to increase this
person's utility from U = 2 to U
3. How much would this subsidy cost the
government? Is the LSP verified in this example?
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