Question

Section B. Short Answer Question (2 questions, 20 points each) Question 1 (20 pts) The following data pertain to products A and B, both of which are purchased by Emily. Emily has $105 to spend per time period. Initially, the prices of the products are PA $5, PB $10. And Emily's optimal consumption bundle is O1 {QA = 5, QB- 8}. 1.1) What is Emily's marginal rate of substitution when she consumes the bundle O1, i.e., ΔΑ MUB MRS MUA ΔΒ 1.2) suppose the utility Emily gets from the optimal bundle O, is 500. Also there are another two consumption bundles that give Emily utility of 500: 02-(QA = 4.5, QB - 10) and O3 {QA = 4, QB= 11. And the marginal rate of substitution associated with these two bundles are 1 and 0.5, respectively We also know that in the second period, there is a reduction in price of B such that the prices are: PA $5, PB $5. And Emily's new optimal consumption bundle is 04 ={QA = 3, QB 18) 1.2.1) what is Emily's marginal rate of substitution when she consumes the bundle 04? 1.2.2) what's change in consumption rate of good B due to the substitution effect? What's the change due to the income effect? 1.3) Is product Ba normal, inferior, or Giffen good? Explain.

Answer 1

. At equilibrium : MRSMUB - PR .: MRS: 0 - 2 121) At equilibriun (04): MASO A . . 2) to compute sulestitution effect he has led the consumer need old . utility u: 500 of new prices PAEPB = 5. That is at substitute equilibrium : MRS. and u = 500 This occurs at bundle O2 Then substitution effect for B is from O, to O2 and income effect is Op to. Os . SE = 10-8 = 2 : : IE = 18 - 10 = 8 . :. TE = 8 + 2 lo 3) In this case, the change in price of increases relative income of the consumer. This is imp The change in consumption due to change in relative income in given as income effect. Hence, as price fall relative income effect is positive this, implies a rise in income increases consumption of B. Then product B is normal good,