A firm is a monopsony in the input market and a perfect competitor in the output market. Its production function is y = x (20 x) /2, for 0 x 10. The supply curve of the input is S : w =1+ x and the price of the output is p = 1.

Find the quantity of input the firm will hire and the input price w it will pay. How would you define the deadweight loss here and what would its value be?