Exam 7: Income and Substitution Effects in Consumer Goods Markets

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A change in the price of one good cannot leave utility unchanged unless the price change is accompanies by a change in income.

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All quasilinear goods are necessities.

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The price of peaches goes up and I observe you buying more strawberries.This implies strawberries must be a normal good.

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Currently.the price of consuming housing Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? to Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? .At the same time, the government lowers the tax on other consumption, lowering the price from Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? to Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? . a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? captures your tastes, and suppose Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? , Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? , Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? , Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? and Currently.the price of consuming housing   is lowered by the fact that home mortgage interest is tax deductible.Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from   to   .At the same time, the government lowers the tax on other consumption, lowering the price from   to   .  a.Write down your original budget constraint assuming the consumer has income I. b.Suppose the utility function   captures your tastes, and suppose   ,   ,   ,   and   .Write out the utility maximization problem for this consumer prior to any policy change.  c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented? .Write out the utility maximization problem for this consumer prior to any policy change. c.How much housing and other goods will this consumer consume prior to any policy change? d.How much would this consumer be willing to pay to get the policy change implemented?

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Suppose a relatively low income family has a monthly budget of $1,000 to allocate between food and a non-food composite good.In this problem, assume food is aggregated into a "composite food" good that is modeled on the horizontal axis, and the non-food composite good is denominated in "dollars of other consumption".The price of food is $10 per unit.Suppose further that this family's tastes exhibit kinks in indifference curves, with one such indifference curve graphed below. Suppose a relatively low income family has a monthly budget of $1,000 to allocate between food and a non-food composite good.In this problem, assume food is aggregated into a composite food good that is modeled on the horizontal axis, and the non-food composite good is denominated in dollars of other consumption.The price of food is $10 per unit.Suppose further that this family's tastes exhibit kinks in indifference curves, with one such indifference curve graphed below.    a.Draw the family's budget constraint and label the optimal consumption bundle. b.Due to unexpected droughts, the price of food rises to $20.A cash subsidy S that leaves our family with the same level of happiness as it enjoyed prior to the price increase is proposed.How much would this subsidy cost for this family? c.An alternative proposal suggests a price subsidy s that lowers the price of food for this family from $20 to ($20-s), with s set sufficiently high to allow the family to reach its original utility level. d.Yet a third proposal suggests a price subsidy that leaves in tact the new price of $20 for the first 20 units of food bought by the family but then lowers the price for this family to $(20-s') while also making the family just as happy as it was before.How high does s' have to be to accomplish this? e.If cost is all you care about, how would you rank these three policies? What if you care about food consumption for this family and believe a policy is better if it results in more food consumption? a.Draw the family's budget constraint and label the optimal consumption bundle. b.Due to unexpected droughts, the price of food rises to $20.A cash subsidy S that leaves our family with the same level of happiness as it enjoyed prior to the price increase is proposed.How much would this subsidy cost for this family? c.An alternative proposal suggests a price subsidy s that lowers the price of food for this family from $20 to ($20-s), with s set sufficiently high to allow the family to reach its original utility level. d.Yet a third proposal suggests a price subsidy that leaves in tact the new price of $20 for the first 20 units of food bought by the family but then lowers the price for this family to $(20-s') while also making the family just as happy as it was before.How high does s' have to be to accomplish this? e.If cost is all you care about, how would you rank these three policies? What if you care about food consumption for this family and believe a policy is better if it results in more food consumption?

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Bottles of Coca-Cola and equally-sized bottles of Pepsi Cola are perfect substitutes for a consumer, but a bottle of Coke costs 10 cents less than bottles of Pepsi.The income effect of a 15 cent increase in the price of Pepsi will be for the consumer to drink less cola.

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Every Giffen good is a necessity but not every interior good is a necessity.

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The price of peaches goes up and I observe you buying fewer strawberries.Which of the following is consistent with this observation:

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Every necessity is a normal good, but not all normal goods are necessities.

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Wholesale clubs charge a fixed monthly fee but then offer goods at discount prices.For purposes of this question, suppose a wholesale club and a supermarket offer the same composite grocery item, with the supermarket charging no fixed fee but a higher price for the item.(Assume no corner solutions.)

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Homothetic goods are neither necessities nor luxuries, but rather lie on the borderline between them.​

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The price of peaches goes up and I observe you buying more strawberries.This implies that strawberries must be an inferior good.

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Income effects are negative for normal goods, and positive for inferior goods.

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The price of peaches goes up and I observe you buying fewer strawberries.This implies strawberries must be a normal good.

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Every luxury good is a normal good but not every normal good is a luxury.

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Suppose the government spends the same for a particular consumer under two different policies: One subsidizes the price of good x while the other is a lump sum subsidy.Which of the following is true.

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Your drink budget is entirely split between bottled water and fancy liqueurs, and your tastes are quasilinear in bottled water.In an attempt to get people to drink more water, the government introduces a subsidy that lowers the price of bottled water. a.In a graph with bottled water on the horizontal and fancy liqueurs on the vertical axis, illustrate your before-subsidy budget and your optimal bundle A. b.As a result of the water subsidy, I notice you consume more fancy liqueur.Illustrate this in your graph using income and substitution effects. c.You and I are good friends, in part because I confided in you some time ago that I, too, have tastes that are quasilinear in water.(Nothing bonds like quasilinearity!) But, after the subsidy is introduced, you observe that I, unlike you, have reduced my consumption of fancy liqueurs.Your other friends claim that this is proof that our friendship is based on a fiction --- that I cannot possibly also have quasilinear tastes.Illustrate in a graph why your friends are wrong. d.If we both have quasilinear tastes, can you explain what the fundamental difference in our tastes is that accounts for the difference in behavior?

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Goods with small substitution effects tend to be normal goods.

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You and I both have homothetic tastes.When the price of peaches goes up, you buy more strawberries and I buy fewer.Which of the following must be true.

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All homothetic goods are normal goods.

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