Let the utility derived from goods X and Y be as follows for a rational individual: Unit of Good TUX TUY 8 utils 5.5 utils 15 ubils 105 utils 21 utils 15 utils 26 utils 19 utils 30 utils 22.5 utls 33 utils 25.5 utls 35 utils 28 uti 36 utils 30 utills 36 utils 31.5 utils I. 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 identiy (i.e. draw) at least two separate indifference curves. Be sure to include the commodity bundles and the total utility. 4. Arrive at the marginal utility structure for each good individually 5. 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: M. 125 : p.. 2% : pp. 1% and draw in a graph (note you will need two separate graphs of this to be placed at the \"top\"). Be sure to identify the consumer equilibrium commodity bindle and the maximum utility. What is the algebraic condition for Consumer Equilibrium? 6. 7. Let the income change such that it falls to M\'- 85. Find the new consumer equilibrium, draw this in one of good? How do we know the original graphs, and under that draw the Engel curve. Is X a normal or inferior this? Write the formula and identify the value of the income elasticity of demand. Let the own-price change such that it falls to p)s 1%. Find the new consumer equilbrium, draw this in one of the original graphs, and under that draw the demand curve. Is X an do we know this? Write the formula and identify the value of the own-price elasticity of demand 8. Let the Cobb-Douglas utility function take the following form: U = f(X-Y) = AX\" Y(1-a) 9. Let A 100 and ·%. Find the MRS 10. Find the original consumer equilibrium using the budget line in #6 above and draw in a graph. 11, Find the new consumer equilibrium using the budget line in #8 above and draw in the same graph. 12. Draw the demand curve under the graph. Write the formula and identify the value of the own-price elasticity of demand.
*For solution to other parts please post as a separate question supposed to solve only four subparts.
1. A commodity bundle consist of the quantity of the two goods that one prefers to consume for example say X is a bundle of goods (x, y).
2. The functional form is U(x, y) =f(x, y). The function f(x, y) can be cobb-douglas, or may be linear in x and y or may be of type where individuals prefers to consume the two goods in fixed proportion.
Cobb-Douglas: U(x, y) = xayb .
Linear or perfect substitute: U(x, y) = ax+by
Fixed proportion or perfect complement: U(x, y) = min{ax, by}.
3.
Unit of good
TUx
TUy
TU
1
8
5.5
13.5
2
15
10.5
25.5
3
21
15
36
4
26
19
45
5
30
22.5
52.5
6
33
25.5
58.5
7
35
28
63
8
36
30
66
9
36
31.5
67.5
4.
Unit of good
MUx
MUy
MU
1
8
5.5
13.5
2
7
5
12
3
6
4.5
10.5
4
5
4
9
5
4
3.5
7.5
6
3
3
6
7
2
2.5
4.5
8
1
2
3
9
0
1.5
1.5
| Unit of good | TUx | TUy | TU |
| 1 | 8 | 5.5 | 13.5 |
| 2 | 15 | 10.5 | 25.5 |
| 3 | 21 | 15 | 36 |
| 4 | 26 | 19 | 45 |
| 5 | 30 | 22.5 | 52.5 |
| 6 | 33 | 25.5 | 58.5 |
| 7 | 35 | 28 | 63 |
| 8 | 36 | 30 | 66 |
| 9 | 36 | 31.5 | 67.5 |
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