Suppose that MUX = Y and MUY = X. The prices of good X and good Y are $5 and $4, respectively. How many units of good X does the consumer buy if she has $410 of income?

She consumes 41 units of good X.

Explanation:

Utility Maximization:

The maximum utility that a consumer derives from the use of a specified amount of a good or service.

Consumer M aximise the utility when following condition is satisfied.

MUx / MUy = Px / Py

Y / X = 5 / 4

4Y = 5X

According to given sitation the budget constraint is

Px (X) + Py (Y) = M

5X + 4Y = 410

Using 4Y = 5X

thus, 5X + 4Y = 410

5X + 5X = 410

10X = $410

X = 41.