The price of cheese rises from $6 to $10 per pound, while the price of wine remains $3 per glass

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The price of cheese rises from $6 to $10 per pound, while the price of wine remains $3 per glass

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The price of cheese rises from $6 to $10 per pound, while the price of wine remains $3 per glass. For a consumer with a constant income of $3,000, show what happens to consumption of wine and cheese. Decompose the change into income and substitution effects.

Explanation & AnswerSolution by a verified expert

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The budget constraint shows the different combinations of goods that a consumer can purchase with a given income.

Explanation
In the above diagram, the horizontal intercept shows the quantity of cheese that a consumer can buy if they spend their entire income solely on cheese. Since the given income is \$3000$3000 and the market price of cheese is \$6$6 per pound, the consumer can buy 500 pounds of cheese.

Similarly, on the graph, the vertical intercept shows the quantity of wine that a consumer can buy if they spend their entire income solely on buying wine. Since the given income is \$3000$3000 and the market price of a glass of wine is \$3$3 , the consumer can buy 1000 glasses of wine.

Slope of a line is the ratio of the change in the vertical distance to the change in the horizontal distance when moving from one point to the other. Similarly, when a person moves from consuming only cheese to only wine, the change in the vertical distance is -1000 glasses of wine and the change in the horizontal distance is 500 pounds of cheese, which makes the slope of the budget constraint, 2 wine glasses per pound of cheese, when the negative sign is ignored. The slope also reflects the relative price of the two goods \left( \frac{\$6}{\$3}=2\right)($3$6​=2).

\begin{aligned} \text{Slope of budget constraint}&=\text{\,}\left( \frac{\text{Change in the quantity of wine}}{\text{Change in the quantity of cheese}} \right) \\ &=\left( \frac{\left( 0-1000 \right)\ \text{glasses of wine}}{\left( 500-0 \right)\text{\,pounds of cheese}} \right) \\ &=-2\ \text{glasses of wine per pound of cheese} \end{aligned}
Slope of budget constraint ​=(Change in the quantity of cheeseChange in the quantity of wine​)=((500−0)pounds of cheese(0−1000) glasses of wine​)=−2glasses of wine per pound of cheese ​
Verified Answer
In the figure, the slope of the line, that is, the budget constraint, is 2, when the negative sign is ignored.

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