Question

A consumer has a demand function for good 2, ?2, that depends on the price of good 1, ?1, the price of good 2, ?2, and income, ?, given by ?2 = 2 + 240 + 2?1. Initially, assume ? = ??2 40, ?2 = 1, and ?1 = 2. Then the price of good 2 increases to ?2′ = 3. a) What is the total change in demand for good 2? [2 marks] b) Calculate the amount of good 1 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 part c) 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] f) Calculate the amount of change in good 1 due to the Slutsky substitution effect of the price change. [2 marks] g) 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] i) Assume well-behaved preferences and draw a diagram, with ?1 on the horizontal axis and ?2 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 line and 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]

Answers for h-k please.

Answer 1

Gven: A consumeohay a demandl funchon fos gcad a xa, that dependy on the Pice of good 4, P, the Price of good a, pa, and income m, given by ag auoaP Hou 8olukon guo +QP mPa & Pa wheoe muo, a atPR) (2a) 2at uoni at Pa a40 чокз Total chorg n demand of -4 Griven budgel 1ine equakon M P Pa a a8 at Pa , 14

at Pa3 =J40 = aT3 X8 at PL (2 C8,8) Tolal dncome to peochay (A)(14,1a) at (r, =2; Pa-) in 0 Tolal dncome oeq.cied to prhau (4,13) at (-a, P) Cx (4 () 64 Lxce income equycd 64-40 24 Exha . Tolal income (M): 64 At Qub Caa) > t 1.257