Cindy consumes goods x and y.Her demand for x is given by x(p_x, m)  0.05m 5.15p_x.Now her income is $419, the price of x is $3, and the price of y is $1.If the price of x rises to $4 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then

A) DI  0.28 and DS  0.52.
B) DI  0.28 and DS  4.88.
C) DI  0.52 and DS  0.52.
D) DI  0 and DS  2.00.
E) None of the above.

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groovy mexican · Accepted Answer

Final Answer : B, Explanation :  Using the formula for the price effect on demand:Price effect = DI + DSWe first need to calculate the initial demand for x:x(p x , m) = 0.05m/(5.15p x )Substituting the values given, we get:x(3, 419) = 0.05(419)/(5.15(3)) ≈ 4.09Now, when the price of x changes to $4, we have:x(4, 419) = 0.05(419)/(5.15(4)) ≈ 3.07The income effect can be calculated by holding the real income constant and assuming the price change is the only factor affecting demand.DI = x(p1, m)/x(p0, m) - 1Substituting the values given, we get:DI = 3.07/4.09 - 1 ≈ -0.25 or -0.28 (rounded to two decimal places)To calculate the substitution effect, we need to adjust the consumer's income to keep her on the same indifference curve relative to the price change.New income = old income - (price change)x(initial quantity purchased)New income = 419 - (4 - 3)(4.09) = 413.76Now we can calculate the new quantity purchased for x at the new price and with the new income:x(4, 413.76) = 0.05(413.76)/(5.15(4)) ≈ 3.08DS = x(p1, m1)/x(p1, m0) - 1Substituting the values given, we get:DS = 3.08/3.07 - 1 ≈ 0.33 or 0.34 (rounded to two decimal places)Therefore, the answer is (B) DI      0.28 and DS      4.88.

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