Question

1. (19 pts) Adrienne and Deepa consume pizza, Z, and cola, C. Adrienne's utility function is UA = Z CA and Deepa' s utility function is U = 29.5C9.5. Adrienne's marginal utility of pizza is MUZ = CA, and her marginal utility of cola is MUS = Z . Similarly, Deepa' s marginal utility of pizza is MU} = -2;0.500.5 and her marginal utility of cola is MUS = -2,5050.5. Their initial holdings of pizza and cola are ZA = 10,CA = 20,2, = 20, C = 10. a) (4 pts) Draw an Edgeworth box for Adrienne and Deepa with width of the box representing quantity of pizza and height of the box representing quantity of cola. Place Adrienne's origin at the lower left corner and Deepa's origin at the upper right corner. Determine the height and width of the Edgeworth box. b) (5 pts) Indicate the initial holdings of pizza and cola in your Edgeworth box. Is the initial allocation of pizza and cola pareto-efficient? Explain. Sketch the consumers' indifference curves that go through the initial allocation. c) (5 pts) Consider a new allocation of the two goods: 2, = 18, = 18, Z) = 12,0p = 12. Is this allocation pareto-efficient? Explain. Sketch the consumers' indifference curves that go through this allocation. d) (5 pts) What is the formula for the contract curve? Indicate the contract curve in your Edgeworth box.

Answer 1

Que1

a) Assuming there is no wasteful allocation,

Width of the box = Za+Zb=30

Height of the box = Ca+Cb=30

$1587852732173_IMG_0394.png$ b) $1587853601503_IMG_1070.png$ Let ICA denote Adrienne's IC and ICB denote Deepa's IC $1587853924980_IMG_1350.png$ C) $1587854265672_IMG_3295.png$ D) Contract Curve $1587855387321_IMG_7011.png$ Hence the contract curve will pass through all th points where Adrienne (or Deepa) consumes same number of pizzas and colas.

Hence if we take adrieene's pizzas as x axis and colas as y-axis the contract curve will be x=y and its slope will be equal to 1.