Question

a consumer utility function is u(x,y)=x1/4 y3/4.given that the consumer has $1000 to spend on the two goods with a price $4 and $3 for x and y respectively. how much should she consume to maximize utility?

Answer 1

So, we have 2 equations:
4x + 3y = 1000
x1/4y3/4 = max
We can state, that x1/4y3/4 = max, when x = 1 and y = (1000 - 4x)/3 = 996/3 = 332
So, the consumer should buy 1 unit of the first good and 332 units of the second to maximize its utility.