Suppose the utility out of two goods x and y is given by U(x, y) = xy. A consumer would like to maximize utility subject to the budget constraint p_xx + p_yy = M.

Using the substitution method, solve explicitly for utility-maximizing basket (x* , y* ).

At that basket, is the utility indeed maximized? Explain.

Write down the equation for indifference curve. Is it convex?