Ron's utility function is given by U(x,y)= min[2x,y]. If the price of x is 1 and the price of y is 1, Ron spends his $12 income on:
A)4 units of x and 4 units of y.
B)8 units of x and 8 units of y.
C)4 units of x and 8 units of y.
D)8 units of x and 4 units of y.

Question

Quizplus · Accepted Answer

Since Ron's utility function is given by U(x,y)= min[2x,y], he would want to maximize the minimum between 2x and y. Given that the price of x and y are the same, Ron would want to choose a combination of x and y such that the ratio of the price of x and y is proportional to the ratio of 2 and 1. In other words, he would want to choose a combination where he spends $2 on x for every $1 he spends on y.

To achieve this, Ron can spend $8 on x and $4 on y. This will give him a total of 8 units of x and 4 units of y. By plugging in these values into his utility function, we can see that Ron's utility will be U(8,4) = min[16,4] = 4.

Any other combination of x and y will either result in a lower utility or will cost him more than $12. Therefore, the best choice for Ron is to spend $8 on x and $4 on y, i.e., he should choose option C.

Ron's Utility Function Is Given by U(x,y)= Min[2x,y]