Understanding Marginal Utility: Income Change with Indifference Curve

University:
Elon University
Course:
ECO 1000 | Economics
Academic year:

2024
Views:

146

Pages:

2
Author:

Masadepan C.

Understanding Marginal Utility: Income Change with Indifference Curve Change in revenue with normal goods case Known: U = f(X,Y) = 20 + 2X + 3XY + 4Y M = 100; Px = 10; Py = 8 MUx = 2 + 3Y MUy = 3X + 4 a. = = 16 + 24Y = 30X + 40 24Y - 30X = 24............... (1) M = X.Px + Y.Py 100 = 10X + 8Y ................. (2) • Equations 1 and 2 are substituted -30X + 24Y = 24 |×1| -30X + 24Y = 24 10X + 8Y = 100 |×3| 30X + 24Y = 300 60X= 276 X= 4,6 • Substitute the value of X into the equation 10X + 8Y= 100 10(4,6) + 8Y = 100 46 + 8Y= 100 8Y= 100 - 46 8Y= 54 Y= 6,75 b. Umax = 20 + 2X + 3XY + 4Y = 20 + 2(4,6) + 3(4,6)(6,75) + 4(6,75) = 20 + 9,2 + 93,15 + 27 = 149,35 c. MUx = 2 + 3Y = 2 + 3(6,75) = 22,25 MUy = 3X + 4 = 3(4,6) + 4 = 17,8 Graph of revenue change with normal goods case Px = 10; M = 100; Py = 8 M = 80M ' = 100 Y1 = 5. 5M/Py = 10 X1 = 3. 6M/Px = 8 Y2 = 6.75M/P 'x = 10 X2 = 4.6M/P 'y = 12.5 y 12,5 10 6,75 5,5 x 3, 64, 6810 Explanatio n: From the curve above, it can be seen that the increase in income affects the consumption power of X and Y. Initially, the consumption of good X is 3.6 and the consumption of good Y is 5.5. Then, the consumption of goods X changes to 4.6 and the consumption of goods Y to 6.75, this incident is in accordance with the definition of normal goods, namely demand will increase when income increases. From this case, the quantity of good X and the quantity of good Y increase due to an increase in income from 80 to 100. The budget line also changes when income is increased. From the curve above, it is known that IC 2 is located above IC 1, which means that IC 2 satisfaction is higher. So, if income is increased, it can lead to an increase in satisfaction.