IV. An upstream monopoly sells the good x to a downstream monopoly. The downstream monopoly uses this good as an input to produce its output y. The production function of the downstream monopoly is y = x. The downstream monopoly sells its output to final consumers whose aggregate demand curve is y = p3. The upstream monopoly's cost function is c (x) = 2x.

a) Find the price k the upstream monopoly charges the downstream monopoly and the price p the downstream monopoly charges the final consumers.

b) Assume the two monopolies merge into a single monopoly that produces y from x internally (according to the same production function) and sells it directly to the final consumers. What will be the price p of the output?