Luis’s utility function is u=x^.4y^.6

Suppose that Luis wants to get 60 utils, provide 4 bundles with which he can achieve that level of utility.
Please explain

To find four bundles with which Luis can achieve 60 utils, we need to solve the utility function equation u = x^0.4 * y^0.6 for different combinations of x and y until we find four bundles that satisfy this equation.

Start by plugging in values for x and y and solve for u:

1. Bundle 1: Let's assume x = 1 and y = 1
Now, calculate u = 1^0.4 * 1^0.6 = 1 * 1 = 1
Since the utility is less than 60, this bundle does not satisfy the requirement.

2. Bundle 2: Let's assume x = 10 and y = 1
Now, calculate u = 10^0.4 * 1^0.6 = 2.512
Since the utility is less than 60, this bundle does not satisfy the requirement.

3. Bundle 3: Let's assume x = 1 and y = 10
Now, calculate u = 1^0.4 * 10^0.6 = 3.981
Since the utility is less than 60, this bundle does not satisfy the requirement.

4. Bundle 4: Let's assume x = 100 and y = 1
Now, calculate u = 100^0.4 * 1^0.6 = 6.310
Since the utility is less than 60, this bundle does not satisfy the requirement.

Repeat this process by trying different combinations of values for x and y until you find four bundles that yield a utility of 60 or more.

To find the bundles with which Luis can achieve 60 utils, we need to set up the utility function and solve for x and y.

Luis's utility function is u = x^0.4 * y^0.6, where x represents the quantity of good x and y represents the quantity of good y.

We want to find bundles (x, y) that satisfy the equation u = 60.

Substituting 60 for u in the utility function, we have:
60 = x^0.4 * y^0.6

To simplify the equation, let's take the natural logarithm (ln) of both sides:
ln(60) = ln(x^0.4 * y^0.6)

Using the properties of logarithms, we can rewrite the equation as:
ln(60) = 0.4 * ln(x) + 0.6 * ln(y)

Now, we have an equation with two variables (x and y). We can solve for y in terms of x or vice versa.

Let's solve for y in terms of x:
0.6 * ln(y) = ln(60) - 0.4 * ln(x)
ln(y) = (ln(60) - 0.4 * ln(x)) / 0.6
y = e^[(ln(60) - 0.4 * ln(x)) / 0.6]

Now, we can choose any value for x and solve for the corresponding y using the equation above.

For example, let's choose x = 1 and solve for y:
y = e^[(ln(60) - 0.4 * ln(1)) / 0.6]
y = e^[(ln(60) - 0) / 0.6]
y = e^[ln(60) / 0.6]
y = e^(1.60944 / 0.6)
y ≈ 6.248

Therefore, one bundle that satisfies the equation u = 60 is (x = 1, y ≈ 6.248).

You can continue this process with different values of x to find other bundles that achieve 60 utils, such as (x = 2, y ≈ 4.191), (x = 3, y ≈ 2.753), and (x = 4, y ≈ 1.811).

These four bundles, (1, 6.248), (2, 4.191), (3, 2.753), and (4, 1.811), are examples of bundles with which Luis can achieve a utility level of 60 utils.