Question

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ECON 2023 Spring 2019: Homework #1 Let the utility derived from goods X and Y be as follows for a rational individual: Unit of Good TUX TU_Y 8 utils 15 utils 21 utils 26 utils 30 utils 33 utils 35 utils 36 utils 36 utils 5.5 utils 10.5 utils 15 utils 19 utils 22.5 utils 25.5 utils 28 utils 30 utils 31.5 utils 2 4 6 8 9 1. 2. What is a 'commodity bundle' (you can assume a two-commodity world)? What is the functional form of the utility function in a two-commodity world? Be sure to identify each element. 3. Assume that the Total Utility from the above is TU, TU+TU,. Construct the Utility Matrix and identify (i.e. draw) at least two separate indifference curves. Be sure to include the commodity bundles and the total utility Arrive at the marginal utility structure for each good individually. What is the income equation and the budget line? Be sure to draw the budget line in commodity space and identify the intercepts and slope. Find the original consumer equilibrium given: Mo-12$ : po: 29, : p. 1%, and draw i will need two separate graphs of this to be placed at the "top equilibrium commodity bin Equilibrium? 4. 5. n a graph (note you 6. dle and the maximum utility. What is the algebraic condition for Consumer 7. Let the income change such that it falls to M-8$. Find the new consumer equilibrium, draw this in one of the original graphs, and under that draw the Engel curve. Is X a normal or inferior good? How do we know this? Write the formula and identify the value of the income elasticity of demand. Let the own-price change such that it falls to pt: 1% Find the new consumer equilibrium, draw this in one of the original graphs, and under that draw the demand curve. Is X an ordinary or Giffen good? How do we know this? Write the formula and identify the value of the own-price elasticity of demand. 8, the Cobb-Douglas utility function take the following form:

Answer 1

1) Commodity bundle (in a 2 commodity world) is a mix of 2 products (say X and Y) that a consumer consumes in different proportions so as to derive satisfaction. Assuming that the money available to buy these 2 products is fixed (Income is fixed), then the consumer will have to reduce 1 quantity of X in order to consume 1 more quantity of product Y.

2) Functional Form of utility in a 2 commodity world

U(x,y) = X +Y

where U represents Utility Function

X represents Commodity X and Y represents Commodity Y

4) Marginal Utility for Product X

Total Utility from X (TUx)	Marginal Utility from X (MUx)
8	-
15	(15-8) = 7
21	(21-15)= 6
26	(26-21)= 5
30	(30-26)= 4
33	(33-30)= 3
35	(35-33)= 2
36	(36-35)= 1
36	(36-36)= 0

Marginal Utility for Product Y

Total Utility from Y (TUy)	Marginal Utility from Y (MUy)
5.5
10.5	(10.5-5.5)= 5
15	(15-10.5)= 4.5
19	(19-15)= 4
22.5	(22.5-19)= 3.5
25.5	(25.5-22.5)= 3
28	(28-25.5)= 2.5
30	(30-28)= 2
31.5	(31.5-30)= 1.5