Question

Problem 1 [32 marks] A consumer has a demand function for good 2, X, that depends on the price of good I. P. the price of good 2. Pz, and income, m, given by xy = 2+ +2P. Initially, assume m= 40, P-1, and P = 2. Then the price of good 2 increases to P = 3. a) What is the total change in demand for good 2? [2 marks] b) Calculate the amount of good I consumed at the optimal bundle before and after the price change. [3 marks] c) What is the amount of income needed to make the initial optimal bundle just affordable at the new prices? [5 marks] d) Find the optimal consumption of good 2 at the income level you found in parte) after the price change. [1 mark] e) Calculate the amount of change in good 2 due to the Slutsky substitution effect of the price change. [3 marks] n Calculate the amount of change in good I due to the Slutsky substitution effect of the price change. [2 marks] 8) Calculate the amount of change in each good due to the income effect of the price change. [3 marks] h) For good 2, check that the Slutsky identity does indeed hold in this example. [1 mark] 1) Assume well-behaved preferences and draw a diagram, with x, on the horizontal axis and Xy on the vertical axis, showing the Slutsky substitution effect and income effect you calculated in parts e) through g). Label the initial budget line, the final budget line, and the line that passes through the initial bundle and is parallel to the final budget line, and show the axis intercepts for each. Show the coordinates of the optimal bundles on each budget ling draw the indifference curves through these optimal bundles. Show the substitution and income effects on both goods with arrows. [6 marks] j) Using your diagram, for each good, determine whether it is an inferior good or normal good. Justify your answer. If there is not sufficient information to determine the type of good, explain why. [3 marks] k) Using your diagram, for each good, determine whether it is an ordinary good or Giffen good. Justify your answer. If there is not sufficient information to determine the type of good, explain why. [3 marks] m =X

only question that is problem is (i) many thanks .

Answer 1

Date Topic mp₂ P, = 2 m = 40 Initial Bundle - x =2 t 240 - (40) (1) + 2x2 Budget line 22, + 2 = 40 = 2 + 6 + 4 =12 12 P, 2 X = no X = 28 x, = 14 (x,x) =(2, 12

Final Bundle (After Price charge) x = 2t 240 + 2x2 (4063) x₂ =2 + 2 +4 = 8 Budget like. 22, + 38 = 40 P, x = m - pix, Pixi = 40 - (3) (8) pix, = 40.-24 2x = 16

Date Topic Intermediate Bundle (the bundle consumed on osigual prices but on income which allows to buy orignal bondie at Bigano) prices) = = (1) (28) + (3) (12) 28 + 36 = 64 At m'=64, consumer can bey orignal bundle at new. prices Consumption at this income Budget live : 27 र, -64 x = + 2x2 2 +240 la3)

consumption at this income 2x, +372 64 x = 2 +240 (64)(3) + 2x2 =2+ 1.25 tu = 7.25 P x = m' - P x PX" = 64 -(3) (7:25) Pix," =64 - 21.75 - - 42.25 = 21.125 24 125 (x",x") = (resos, 7.25)

Date Topic Substitution Effect - x - x, = = 7.25 - 12 -4.75 Income Effect = = = x - x 8 - 7.25 0.75

Topic Initial Budget Lins cbbcd 40 - Final Budet DC effect o

Blue line - intermediate budget line