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Prove that price effect =income effect +substitution effect through graphical representation

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section: Chapter Questions

Problem 7SQP

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Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?
a) Explain by using an example why an MRS (Marginal Rate of Substitution) between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction?
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The owner of Grand Central Bookstore is looking into the sales of its Health & Fitness magazine section. She finds that her equilibrium is at 800 magazines per month sold at an average price of $4.75 per magazine. When the price of these Health & Fitness magazines rose to $5.00 each, the quantity sold fell to 725 magazines per month, while the quantity supplied to her increased to 900 a month. From the scenario described, answer the questions below. Draw an appropriate graph for Grand Central’s Bookstore’s to illustrate this change in the Health & Fitness magazines market position when the price rises to $5.00. Calculate the price elasticity of demand for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know? Calculate the price elasticity of supply for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know based on your answer? The owner also noticed that…
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3. Consider the following model. U(X,Y)= X2$Y35 Px =2 Py = 3 I= 100 Suppose price of X changes to Px= 4. What are the substitution effect and income effect on Y?
Consider a consumer buying perfect complements. If there is a decrease in the price of good 1, the total change in consumption of good 1 is due to (a) the pure substitution effect (b)the pure substitution effect minus the income effect (c)the income effect (d)it depends on whether the good is inferior or normal (e) none of the above.
What are the examples of complement and substitute goods, where a change in price of one good would cause a change in demand of the other good? Show Graphically.
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Suppose that beer and pretzels are unrelated goods (neither complements nor substitutes). Which of the following must be true? The substitution effect of a decrease in the price of beer on pretzel consumption is smaller than offsets the income effect on pretzel consumption The substitution effect of a decrease in the price of beer on pretzel consumption is larger than the income effect on pretzel consumption The substitution effect of a decrease in the price of beer on pretzel consumption exactly offsets the income effect on pretzel consumption There is no substitution effect on pretzel consumption for a decrease in the price of beer
Suppose a consumer has preferences between two goods that are perfect substitutes. Can you change prices in such a way that the entire demand response is due to the income effect?
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