Hello! I'd like to know the quote for receiving help on this assignment. Thank you.
Concordia University —Econ 301 Winter 2023 Assignment 3 • The due date is Monday, March 27. • The total is 113 points. • Justify your answers. 1. (89 points) Elasticity, Slutsky, compensating and equivalent variations Ike has utility function u (x1, x2) = x1x2 where x1 and x2 are his consumptions of goods 1 and 2, respectively. He has a budget m to spend entirely on goods 1 and 2 who’s prices are p1 and p2. a) (4 points) Compute Ike’s ordinary demand for good 1 and 2: x1(p1, p2,m), x2(p1, p2,m). Show the main steps. (note, make sure this is correct as it will be used extensively in the following exercises). b) (6 points) Compute Ike’s i) own-price point elasticity of demand of good 1 (ε1,1), ii) cross-price point elasticity of demand for good 2 with respect to the price of good 1 (ε1,2), iii) income point elasticity of demand of good 1 (label it η1). Use derivative for your calculations. Simplify as much as possible. Note: use derivatives. c) (5 points) Only based on your previous calculations at b), what do you conclude about the nature of goods 1 and 2 (ordinary / normal / inferior / Giffen / luxury / complement / substitute). Say as much as possible. d) (2 points) Ike’s budget is m = 8 and the initial prices of goods 1 and 2 are p1 = 2, p2 = 2. How much is Ike consuming of good 1 and good 2? Label this initial consumption bundle ( xA1 , x A 2 ) . e) (2 points) If the price of good 1 doubles to p′1 = 4, what is Ike’s new consumption bundle? Note it ( xB1 , x B 2 ) . 1 f) (3 points) Compute the own-price arc elasticity of demand ε1,1 between ( xA1 , x A 2 ) and( xB1 , x B 2 ) .? g) (3 points) What income would Ike need in order for him to be able to consume his old bundle ( xA1 , x A 2 ) at the new prices (p′1, p2) = (4, 2)? Note this compensated income m ′. h) (2 points) If Ike had income m′ (instead of m = 8) and the prices were the new prices (p′1, p2) = (4, 2), what would be his optimal consumption choice? Note this compensated bundle ( xC1 , x C 2 ) . i) (6 points) The whole Slutsky decomposition can be expressed as ∆x1 = ∆ sx1 + ∆ mx1 where • ∆x1 is the change in consumption of good 1 following the change in price from p1 = 2 to p′1 = 4. • ∆sx1 is the substitution effect. • ∆mx1 is the income effect. Find ∆x1, ∆sx1 and ∆mx1. j) (20 points) Represent on a graph: • The three bundles, ( xA1 , x A 2 ) , ( xB1 , x B 2 ) , and ( xC1 , x C 2 ) • The initial budget constraint, the final budget constraint (with m and p′1), and the compensated budget constraint (with m′ and p′1) • The approximate indifference curves passing through each bundles. They do not have to be mathematically exact, but be sure they make sense given Ike’s consump- tion choices. • The total effect ∆x1, the substitution effect ∆sx1, and the income effect ∆mx1. Be sure to show the important number on the axes. k) (4 points) What was Ike’s utility level when consuming his initial consumption bundle UA = u ( xA1 , x A 2 ) ? What is Ike’s utility level after the price change UB = u ( xB1 , x B 2 ) ? l) (6 points) How much money must we give to Ike in addition to his initial budget m = 8 so that he obtains his initial utility level UA when the prices have changed to (p′1, p2) = (4, 2)? Call this extra amount of money CV, for compensating variation. With this money, what would be Ike’s consumption bundle? Call it ( xD1 , x D 2 ) . Note, it’s possible you don’t get whole numbers as solutions. Just simplify as much as you can, but do not compute square roots. m) (6 points) How much money must we remove from Ike’s budget of m = 8 so that, at initial prices (p1, p2) = (2, 2), he obtains the utility level UB when the prices have 2 changed? Call this money to be removed EV , for equivalent variation. With this money removed and at the initial prices, what would be Ike’s consumption bundle? Call it( xE1 , x E 2 ) . Note, it’s possible you don’t get whole numbers as solutions. Just simplify as much as you can, but do not compute square roots. n) (20 points) Represent on a graph: • The bundles, ( xA1 , x A 2 ) , ( xB1 , x B 2 ) , ( xD1 , x D 2 ) , and ( xE1 , x E 2 ) . • The initial budget constraint, the final budget constraint (with m and p′1), and the compensated budget constraint (for the compensated variation) and the equivalent budget constraint (for the equivalent variation) • The approximate indifference curves passing through each bundles. They do not have to be mathematically exact, but be sure they make sense given Ike’s consump- tion choices. Be sure to show the important number on the axes. 2. (24 points) Demand aggregation Stan and Wendy consume candies. Stan’s inverse demand for candies is pS(q) = 10− q Wendy’s demand is pW (q) = 8− 2q a) (8 points) Find their aggregate inverse demand p(q). Be sure to describe all the segments and their limits accurately. b) (6 points) If the price rises from p = 7 to p = 9, what is the impact on the consumer surplus of Stan and Wendy? c) (10 points) Draw the aggregate inverse demand on a graph, showing all relevant values on the axes. Show the loss in consumer surplus when the price rises from p = 7 to p = 9. 3