For both questions below let's assume there are two monopolies: Upstream and downstream monopoly. The upstream monopoly sells yarn to a downstream monopoly and the downstream monopoly uses this yarn as an input to produce output (cloth) y. The downstream monopoly then sells that (cloth) output to its customers and has a production function of y=x. The upstream monopoly's cost function is c(x)= 2x. The agg. demand curve of the customers is y= 12-p

1. What is the price k charged by the upstream monopoly to the downstream monopoly for the yarn. What is the price 'p' that the down stream monopoly chargers their customers.
2. Find the quantity of input x (yarn) the upstream monopoly sells to the downstream monopoly. Find the quantity of output y (cloth) sold to customers.
3. If the monopolies were to merge into one monopoly to produce an output (cloth)y from input x(yarn) and choose to sell their goods directly to the final customer, what is the quantity y and the price p of the output ? What is the profit of the merged monopolies?