The technology of the final goods sector is given by: Y=N". N >1, 12, (Q12.1) where Y is output, X; is the amount of input i used in production, and N is the number of input varieties. The price of input i is denoted by P; so that total cost is equal to: N TCY = . i=1 The firm is a cost minimizer. (Q12.2) (a) Prove that the production function (Q12.1) features constant returns to scale. (b) Prove that the production function features returns to specialization, provided n>1.