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# steps - variable Set utility equal to your original utility...

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Department of Economics University of California, Berkeley Econ 100A, Sections 104 and 108 GSI: Ana Rocca Steps for finding optimal consumption bundle. 1. Find the marginal utility of each good by di ff erentiating the utility function with respect to your chosen variable. 2. Set the MRS ( MU X MU Y ) equal to the price ratio ( P X P Y ) and solve for one of your variables in terms of the other. 3. Plug this expression into the budget constraint and solve for your remaining variable. 4. Go back to your expression in step 2 and use the value you found in step 3 to solve for the amount of the other good. Steps to finding the Substitution and Income e ff ect. 1. Find the optimal consumption bundle before the price change (see above) and solve for the level of utility from consuming this bundle. 2. Find the new tangency condition (under the new prices) by setting the MRS equal to your new price ratio. 3. Solve for one of your variables using this new condition. 4. Using your utility function, plug in this new expression so that you have utility in terms of only one
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Unformatted text preview: variable. Set utility equal to your original utility level (before the price change) and solve for your variable. 5. Go back to your equation from step 2 to solve for the other variable. These values give you the decomposition bundle. 6. The substitution e±ect is given by the change from your original bundle to this decomposition bundle. 7. The income e±ect is given by the change from the decomposition bundle to the ﬁnal bundle. 8. The ﬁnal bundle is found by ﬁnding the optimal bundle for the new prices (see above) and the new budget constraint equation. Remember: the substitution e±ect is always negative for a price increase (since relative price and quantity are negatively related). The direction of the income e±ect depends on whether the product is a normal or inferior good (with more money, are you going to buy more or less of the good). 1...
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