Answer to Question #281718 in Microeconomics for rangga kelana

Question

Let the price of pizza (X) is $2 per unit and the price of shakes (Y) is $ 1

per unit. The budget is $ 38. Marginal utility of X is MUx = 100 – 10x,

marginal utility of Y is MUy = 80 – 10y. Find:

How many of quantity of each item should be purchased in order to get

a maximum satisfaction.

Answer 1

Solution:

To find the consumption bundle that maximizes utility, first recognize that it is one in which the slope of the indifference curve (MUx/MUy) equals the slope of the budget line (Px/Py).

$\frac{100 - 10x}{89 - 10y}= \frac{2}{1}$

$\frac{10 - x}{8 - y}= 2$

X = 2y – 6

Substitute in the budget constraint:

2x + y = 38

2(2y – 6) + y = 38

4y – 12 + y = 38

5y = 38 – 12

5y = 26

Y = 5.2

X = 2y – 6 = 2(5.2) – 6 = 10.4 – 6 = 4.4

X = 4.4

To get maximum satisfaction, the consumer must purchase 5.2 units of pizza and 4.4 units of shakes.