Suppose a person has a utility function U=YX. What is the minimum level of income required to get a utility of 20? Your answer should be a function of, among other things, Px and Py.
To determine the minimum level of income required to achieve a utility of 20, we need to utilize the utility function U = YX, where Y represents income and X represents the consumption of another good.
First, let's set up the equation to find the utility level of 20:
20 = YX
Now, we need to relate this utility equation to the prices of the two goods, Px and Py. Assuming that Px represents the price of good X and Py represents the price of good Y, we can rewrite the equation in terms of these prices:
20 = (Y/Py) * (X/Px)
To find the minimum level of income required, we need to determine the values of Y and X that satisfy the above equation when the utility is equal to 20.
For simplicity, let's assume that Py and Px are constants.
We can solve for Y in terms of X:
Y = (20 * Py * Px) / X
Now, we need to determine the minimum level of Y that satisfies the equation Y = (20 * Py * Px) / X, in order to achieve a utility of 20.
The minimum level of Y occurs when X is at its maximum. Assuming X is a positive quantity, we can set X to infinity:
Y = (20 * Py * Px) / infinity
Since dividing by infinity results in 0, the minimum level of Y required to achieve a utility of 20 is 0.
Therefore, no specific level of income is required to achieve a utility of 20 with the given utility function U = YX.