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 = 12 p. The upstream monopoly's cost function is c (x)=2x.

1. Find the quantity x the upstream monopoly sells to the downstream monopoly and the quantity y the downstream monopoly sells to the 1 final consumers. Find also the price k the upstream monopoly charges the downstream monopoly and the price p the downstream monopoly charges the final consumers. Compute the profits of each monopoly.