1. Suppose we have the utility function, U = XY + X + Y.
a. Find the function for the marginal rate of substitution.
1.). a.). MRS =
MUx = = Y + 1
MUy = = X + 1
MRS = = Y + 1/ X + 1
MRS Function = Y + 1/ X + 1
1.). Budget constraint: I = PxX + PyY
18 = 2X + 4Y
Set MRS =
Substitute in the budget constraint to get X:
18 = 2X + 4Y
18 = 2X + 4()
X = 5
Y = 2
The utility maximizing consumption bundle = (5, 2)
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