Question

For each of the long-run total cost functions given below, determine the average cost function and state what type of returns to scale the firm experiences:
a. ?RTC = 100Q
b. ?RTC=3Q2+Q
c. LRTC=200Q−Q2

Answer 1

a) LRAC = LRTC / Q = 100Q / Q = 100

Since LRAC is constant, as out put increases, therefore, the firm experiences constant returns to scale.

b) LRAC = LRTC / Q = (3Q² + Q) / Q = (3Q² / Q) + (Q / Q) = 3Q + 1

Here, as output (Q) increases, the LRAC will increase, therefore, the firm experiences decreasing returns to scale.

c) LRAC = LRTC / Q = (200Q - Q²) / Q = 200Q / Q - (Q² / Q) = 200 - Q

Here, as output (Q) increases, the LRAC will decrease, therefore, the firm experiences increasing returns to scale.