Frieda, a rational consumer can buy an x-commodity and a y-commodity. Her preferences over alternative (x,y) bundles are given by the utility function
u(x,y)=xy+x^(1/2)
a. At any bundle (x,y), find a formula for the marginal utility of x (which we have called MUx) and a formula for the marginal utility of y(MUy) (Calculus reminder, the derivative of z^(1/2)=1/[2(x)^(1/2)]
b. Using what you just found, give a formula for the marginal rate of substitution of for y at any bundle (x,y) (Our shorthand for marginal rate of substitution is MRSxy)
c. As we go down on e pf Frieda's indifference curves(in the direction of increasing x), does the curve flatten out? use your formula for MRSxy to answer this.
d. Now suppose that the price of x is 1 and the price of y is 2. We see that Frieda chooses a bundle in which the quantity of x is 4. How much is the quantity of y that she chooses what is her income?