Answer:
(b) more than twice as much y as x
Explanation:
At all incomes for which Harold consumes positive amounts of both goods, he will consume more than twice as much y as x.
To see this, we can consider the budget constraint that determines the amount of x and y that Harold can afford to consume. Let I be Harold's income and px and py be the prices of x and y, respectively. Then the budget constraint can be expressed as:
I = px * x + py * y
Substituting the given values for I, px, and py, we get:
I = 1 * x + 2 * y
This equation represents a line in the xy-plane, with slope -2 and y-intercept I/2. This line represents the set of all combinations of x and y that Harold can afford to consume, given his income and the prices of x and y.
Since the utility function U(x,y) = (x+3)(y+2) is a positive linear transformation of x and y, it follows that the slope of the budget constraint will be equal to the slope of the indifference curve at any point on the budget constraint. Therefore, the slope of the budget constraint (-2) represents the relative amounts of x and y that Harold will consume.
Since the slope of the budget constraint is negative, Harold will consume more y than x. Moreover, since the absolute value of the slope is greater than 1, Harold will consume more than twice as much y as x.
Therefore, the correct answer is (b) more than twice as much y as x.
I hope this helps! Let me know if you have any other questions or need further assistance.