Suppose Firm C is an automobile manufacturer. Firm C can use workers (N) and/or automated robots (K) to assemble auto parts and produce cars (Q). For simplicity, assume that the cost of procuring auto parts is zero so that we can focus solely on the assembly stage.

Firm C's production function to assemble a car using workers and robots can be expressed as below.

Q = 10 (N + 2.5K).

The cost of hiring one worker is w and the cost of using a robot is r. Therefore, Firm C's total cost can be expressed as wN + rK. The price of a car is normalized to p=1.

a) Draw Firm C's isoquant when Q=50. Place N on the x-axis and K on the y-axis. Furthermore, denote at least one pair of (N, K) coordinates on your isoquant (just drawing the shape of an isoquant is insufficient). (3 points)

b) Suppose w=1 and r=3. What is Firm C's cost-minimizing input choice (N*, K*) in order to produce Q=50? You need to explain your reasoning (either by logic/math/graphs) behind

your answer. (2 points)

c) Suppose w=1 as in part (b), but it becomes cheaper to adopt robots such that r=1. Conditional on Firm C producing Q=50, how would this affect Firm C's labor demand? What would be the number of robots that Firm C uses? (2 points)