Question

1. The following total utility schedule (Table 3) of Maria who is consuming goods X and Y when the price of X is $6 and the price of Y is $30. Maria's income is $144. 2 46 3 62 4 | 74 5 80 6 84 Table 3 Ox 1 TUX 28 MUX 28 Qy 1 TUY 150 MUX 150 2 270 3 360 4 420 7 480 450 470 b. Are these preferences consistent with the law of diminishing marginal utility? Explain briefly. (10 points) C. How much of X and Y should Maria consume in order to maximize her utility? (10 points) d. For the utility-maximizing bundle of goods X and Y. how much is she spending on X and Y? (10 points) e. Now suppose the price of good X increases to $8. What is her new utility - maximizing bundle of goods X and Y? (10 points) f. Draw Maria's demand curve of good X. Make sure you label the axes. (5 points)

Answer 1

&X i 1 2 3 TUM: 28 46 62 MUA: 28 18 16 4 5 6 7 74 80 84 86 12 6 4 2 gy: 1 2 3 4 5 6 7 Tuy : 150 270 360 420 450 470 480 Muy : 150 120 90 60 30 20 10 (b) Yes these preferences are consistent with the law of diminishing marginal utility - We can see that invieasing the quantity of x or y or both is increating the utility but this increment is decreasing with increasing quantity (c) Budget constraint of Marria is PA ext Py. Y = 'Income - 6x + 30y = 144 At utility maximizing bundle the following condition must hold: ----- Mux a b = 1 MUN. 30 s

This condition is satisfied for four values of X and y (x=y - 4, 5, 6,7) But the value which also satisfies the budget constraint is x=y=y. (d) At this utility maximizing bundle she is spendling $6 4 4 9 = $24 on good x and $30x4 = $120 on good Y.