To solve this problem, we will use the marginal rate of substitution (MRS) to find the indifference curve. The MRS is calculated by taking the derivative of the total utility function with respect to X, which is the good the consumer is willing to give up, and Y, which is the good the consumer is looking to acquire.
The MRS can be calculated as follows:
MRS = (√X² + y²)/2x
By substituting in the total income and the price of goods X and Y, we can calculate the MRS.
MRS = (√200² + 4²)/2*3 = 6/6 = 1
The MRS is equal to 1, meaning that the consumer is willing to give up one unit of good X to acquire one unit of good Y. Thus, the indifference curve is negatively sloped to the right.