Question

2 Aggregate Demand Curves (4 points) Ariadne and her three sisters all have the same preferences, described by the utility function u(z,y) = 2,2y4. The budget constraint for each sister is Is = prz +Pvy, where Is is the sis- ter's income. The demand functions of each sister are given by s Is/(3pz) and ys 2Is/(3p). (a) What is the aggregate demand function for good z, if Ariadne has an income of $30 and her three sisters Bianca, Clara, and Diana have incomes of $60, $90, and S120, respectively? (1) (b) What is the aggregate demand at a price of p 10? (1) Hint: Figure out how many (small) units less of y she has to buy to keep utility constant (c) How does aggregate demand for good change if the income of each sister increases by 10% (d) How does aggregate demand for good z change if the price of good y increases by 10%? (1)

Answer 1

"We concede that above problem the demand curve is given by "" xs = 1s/(3 times p_x) and the same of y is ys = 2 times Is/(3 times py) rightarrow where ""1s"" is a income of individual sister�s rightarrow The aggregate demand for x is given by x = x_1 + x_2 + x_3 + x_4 = 151/(3 times p_x) + 152/(3 times p_x) + 153/(3 times p_x) + ISA/(3 times p_x) doublerightarrow x = (1s1 + 1s2 + 1s3 + 1s4)/(3 times p_x) rightarrow Now 1s1 = 30 1s2 = 60 1s = 90 1s4 = 120 rightarrow than sum of all income be 1 = (1s1 + 1s2 + 1s3 + 1s4) = (30 + 60 + 90 + 120) = 300 so x = 300/(3 times p_x), doublerightarrow x = 100/p_x -(1)eq Than, if p_x = 10, so price = x = 100/p_x doublerightarrow x = 100/10 = 10 "