Question
Aiden has the following utility function: U ( x, y ) = 4 y + 2x 0.5 . Let px and py be the corresponding
Aiden has the following utility function: U(x, y) = 4y + 2x0.5. Let pxand pybe the corresponding prices and I his income.
a) Setup the Lagrangian function and Find the first-order conditions (FOCs). Use these FOCs to find the expression for the marginal rate of substitution (MRS). What do you think is special about this indifference curve?
b) Find the demand functions for x and y.
c) Suppose Aiden lives in a city where px= 1, py= 4 and his job offers him I = 20. Find the optimal consumption. Now suppose he is offered a new job that offers him an income of 25 (I = 25) but the job is in another city with px=2, py= 4. Should he take the job? Answer by comparing the utilities.
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Microeconomics
Authors: Robert Pindyck, Daniel Rubinfeld
8th edition
978-0132870436, 132870436, 013285712X, 978-0133371178, 133371174, 978-0132857123
