Suppose that you have the following utility function U(x,y) = 6x^(0.5) + y

The price of x is px and the price of y is 1.

a) Your income is Y = $24. Find the uncompensated demand for good x. That is, find the amount of x which maximises the consumer's utility subject to affordability. Do not worry about corner solutions.

b) What is the income elasticity of uncompensated demand for good x?

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 minimises your expenditure, subject to attaining utility of 10. Do not worry about corner solutions.