Consider two firms that operate in perfect competition with different levels of technology.

Consider two firms that operate in perfect competition with different levels of technology. Firm i maximizes profits using technology yi = zik α i each period by renting capital ki with the rental price R, where α ∈ (0, 1) determines the returns to scale. Firm j also maximizes profits using technology yj = zjk α j each period by renting capital kj with the rental price R, where α ∈ (0, 1). When zi > zj holds, would an efficient allocation of capital across firms be ki > kj? State your answer and prove it formally (mathematical derivations are required and you are not allowed to skip any necessary steps).