Solve the following optimization problem using Lagrange's method
Max U(x, y) = 3³√x √y
Given that px+qy=m
The function U (x, y) can be regarded as the utility function of an individual, where x and y are consumed by respectively item 1 and 2 respectively. The subsidy condition represents the consumer's budget condition, where p and q are prices for goods 1 and 2 respectively and m is the consumer's income.
b) Use the solution found in a) to show how the following changes affect demand for the two items:
i) increased price of item 1 (increased p)
ii) increased income (increased m)
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