Consider a utility function l(X_{A}, X_{B}) = X_{A}X_{B} Let P_{A} =\$3 and P_{B} =\$2. and income is set at M =\$40. Suppose P_{B} falls to P_{B}' = 1 1. Before the price change, what was x_{A} ^ and x B^ * the optimal consumption bundles? Sketch the original budget line and label the point ( x_{A} ^ * ,x B ^ * ) as A. Let x_{A} be on the horizontal axis. 2. If, after the price change, income changed so that the original optimal bundle is just as affordable. What is the new income, m' ? At (p_{A}, p_{B}', m') what is the new optimal bundle (x_{A}', x_{B}')' Sketch the budget line associated with p_{A}, p_{B}', m' ) . Label the point (x_{A}', x_{B}') as B. 3. Does the substitution effect result in more x_{B} ? How many more or fewer? 4. After the price change, how much x_{A} and x_{B} are actually bought. ( x_{A} ^ prime prime ,x B ^ prime prime )? Sketch the budget line associated with (p_{A}, p_{B}', m) Label the point x_{4} ^ prime prime , x_{R} ^ prime prime ) as C. 5. Along the vertical axis, label the income effect, the substitution effect, and the total effect on the demand for x_{B} 6. The income effect of the fall in p_{B} is the same as an (increase, decrease) in income of $. (Choose "increase" or "decrease" and supply the missing value.) Does the income effect result in an increased consumption of x_{B} How much more? 7. Does the substitution effect of the fall in p_{B} make the consumer consume more or fewer x_{A} ? How much more or fewer? Does the income effect of the fall in the price of x_{R} make the consumer consume more or fewer x_{A} ? What is the total effect of the change in the price of x_{B} on the demand for x_{A} ?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a utility function l(X_{A}, X_{B}) = X_{A}*X_{B} Let P_{A} =\$3 and P_{B} =\$2. and income is set at M =\$40. Suppose P_{B} falls to P_{B}' = 1 1. Before the price change, what was x_{A} ^ * and x B^ * the optimal consumption bundles? Sketch the original budget line and label the point ( x_{A} ^ * ,x B ^ * ) as A. Let x_{A} be on the horizontal axis. 2. If, after the price change, income changed so that the original optimal bundle is just as affordable. What is the new income, m' ? At (p_{A}, p_{B}', m') what is the new optimal bundle (x_{A}', x_{B}')' Sketch the budget line associated with p_{A}, p_{B}', m' ) . Label the point (x_{A}', x_{B}') as B. 3. Does the substitution effect result in more x_{B} ? How many more or fewer? 4. After the price change, how much x_{A} and x_{B} are actually bought. ( x_{A} ^ prime prime ,x B ^ prime prime )? Sketch the budget line associated with (p_{A}, p_{B}', m) Label the point x_{4} ^ prime prime , x_{R} ^ prime prime ) as C. 5. Along the vertical axis, label the income effect, the substitution effect, and the total effect on the demand for x_{B} 6. The income effect of the fall in p_{B} is the same as an (increase, decrease) in income of $. (Choose "increase" or "decrease" and supply the missing value.) Does the income effect result in an increased consumption of x_{B} How much more? 7. Does the substitution effect of the fall in p_{B} make the consumer consume more or fewer x_{A} ? How much more or fewer? Does the income effect of the fall in the price of x_{R} make the consumer consume more or fewer x_{A} ? What is the total effect of the change in the price of x_{B} on the demand for x_{A} ?

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