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Bob’s preferences are described by the following utility function: u(x,y)=8x^0.5+y 1. Derive bob’s marginal rate of...

Bob’s preferences are described by the following utility function:

u(x,y)=8x^0.5+y

1. Derive bob’s marginal rate of substitution (MRS)

2.Is this preference homothetic? Explain your answer for full credits. Be sure to explain what homothetic preference means.

3. Does this preference have the characteristic of diminishing marginal rate if substitution?

4. Suppose Bob's income is w=400 and px=4. Use Bob's MRS to find the range of py where Bob wants to consume zero amounts of y

5. Suppose Bob’s income is w=400 and Py = 5. Use bob’s MRS to find the range of Px where Bob wants to consume zero amounts of x

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