Question

Consider a firm that operates using only a single variable input, labor (denoted ℓ). The production function of this firm is given by:
Φ(ℓ)=?=2√ℓ
where ? denotes output. The firm is a price-taker in both the output market and the input market for labor. Each unit of labor costs the firm ?>0. The market price for the firm’s output is given by ?>0.
(a) Show that the firm’s total cost function is ??(?;?)= (?/4)?² and  Show that the firm’s profit function is ?∗(?,?)=?²/w
(b) Derive the firm’s supply function, ?∗(?,?). and  Derive the firm’s (unconditional) labor demand function, ℓ∗(?,?). Show that ℓ∗(?,?) is homogenous of degree zero (with respect to output and input prices) and interpret

Answer 1