Suppose that you have the following utility function: *U*(*x*, *y*) = 6*x*0.5 + *y*.The price of *x *is *px *and the price of *y *is 1. Your income is

*Y *= $36.

a, Find the uncompensated demand for good *x*. That is, find the amount of *x *which maximizes your utility subject to your budget constraint. Note that the answer will be an expression that contains *px *. You can use any method you want. Do not worry about corner solutions.

b,What is the price elasticity of uncompensated demand for good *x *when *px *=3?

c,Now suppose that you want to attain utility *U *= 10. Find the compensated demand for good *x*. That is, find the amount of *x *which minimizes your expenditure subject to your utility constraint. Note that the answer will be an expression that contains *px *. You can use any method you want. Do not worry about corner solutions.

d. How does the expression you obtained in part (a) compare to the expression you obtained in part (c)? Explain.

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