If the utility function is: U=58×1 + 6×2 How many units of x1 is the consumer willing to pay to get 15 more unit of x2? (hint: careful on this one, read it carefully, it is NOT asking you how many units of x2 for one extra unit of x1. Remember how to obtain the opportunity cost of x2 using MRS.)
MRS = MUx1/ MUx2
MUx1 = ∂U/∂x1
= ∂ (58×1 + 6×2)/ ∂ x1
MUx2 = ∂U/∂x2
= ∂ (58×1 + 6×2)/ ∂ x2
MRS2 = 58/6 = 9.67
In order for the consumer to consume an extra unit of X2, he has to give up 9.67units of X1
1 = 9.67
15 = (15 ×9.67)/ 1 = 145.5 units of X1 need to be given up in order to consume an extra 15 units of X2.
MRS1 = 6/58 = 0.103
In order to consume an extra unit of good X1the consumer will have to give up 0.103units of good X2. This means that in order for the consumer to get an extra 15 units of X1
1 = 0.103
15 = (15 × 0.103)/ 1 = 1.55 units of X2 have to be given up in order to consume an extra 15 units of X1.
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