Consider a firm having the production function

Y=K0.5(EN)0.5

Assume a fixed stock of capital =1, a fixed technology=1

E=1, and the demand schedule Dj=AlogPj

implying a constant mark-up. Let denote the price of labour and the rental rate of capital.

Given that we use the inverse demand function, we can write the profit of firm-

jas follows:

j=A1Dj11rwNj

We can maximise the firm's profit with respect to the amount of firm's output, Dj

(Note thatisYin a general form of the production function here.)

What is the first order condition (expressed in terms of the price?

Select one or more

1. (11)Pj=2wNj0.5
2. (11)Pj=2wNj0.5
3. (1+1)Pj=2wNj0.5
4. (1+1)Pj=2wNj0.5