Respuesta :
Answer:
2 units of X and 5 units of Y
Step-by-step explanation:
(a) Utility is maximized when (MUx / Price of X) = (MUy / Price of Y)
This condition holds for the following cases
1. X = 4 (MUx / Px = 8 / 4 = 2) and Y = 6 (MUy / Px = 4 / 2 = 2)
2. X = 2 (MUx / Px = 16 / 4 = 4) and Y = 5 (MUy / Px = 8 / 2 = 4)
For the first case Total cost = 4 x $4 + 6 x $2 = $(16 + 12) = $28 (Budget is exceeded).
In the second scenario, Total cost = 2 x $4 + 5 x $2 = $(8 + 10) = $18 (budget is exhausted).
Optimal case contains X = 2 units, Y = 5 units.
The quantities of each of x and y that we will purchase to maximize the utility are 2 'x' quantities and 5 of 'y' quantities.
How to maximize the utility?
The utility of two products x and y are maximized when:
[tex]\dfrac{\text{MU of x}}{\text{Price of x}} = \dfrac{\text{MU of y}}{\text{Price of y}}[/tex]
where MU denotes Marginal Utility.
For the considered case, we're specified that:
- Amount of income = $18
- Price of x = $4.00 each
- Price of y = $2.00 each
From the table which is missing from the problem, two values pair satisfy the condition for maximizing the utility.
They are at 4 quantities of x and 6 quantities of y or, 2 quantities of x and 5 quantities of y.
For the first case;
[tex]4 \times 4 + 6 \times 2 = 28 > 18[/tex]
The condition of maximizing utility with the amount being under or equal to $18 is satisfied at 2 quantities of x and 5 quantities of y.
[tex]2 \times 4 + 5 \times 2 = 18[/tex] (in dollars)
Thus, the quantities of each of x and y that we will purchase to maximize the utility are 2 'x' quantities and 5 of 'y' quantities.
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