3. (2 points + 1 bonus point) Suppose Firm A and Firm B are both in the same product market that is perfectly competitive. Each rm's production function can be expressed as follows: Firm A: Q = N%K% Firm B: Q = Nae a) (0.5 points) Derive the marginal rate of technical substitution (MRTS) for Firm A and B. b) (0.5 points) Based on your derivation in part (a), which of the following statement is incorrect? a. At a given point (N ,K), Firm A's MRTS is higher than Firm B's. b. At a given point (N ,K), Firm A will substitute a unit of labor with capital at the same rate that Firm B does. c. Firm A and Firm B's MRTS only depend on the ratio of K and N. (1. None of the above. 0) (1 poin Suppose p=1, w=1, and 1:1. Derive the prot-maximizing input combination (N *,K') for Firm B. d) (1 bonus point) This is a bonus question. There is no penalty for not solving this question. Now assume that w=1 and r=1, but p=p1 (p1 is a positive constant which may or may not equal to 1). Derive the prot-maximizing input combination (N '",K*) for Firm A for each of the following scenarios. Make sure to explain your reasoning. a. p12