Question

A University's food services produces 'square meals' (SM) using only one input,

'unmentionable' (U), and a remarkable production process. The production function is:
SM = U²

Part 1. This production function exhibits Increasing, Decreasing/Diminishing or Constant returns to scale?    

Part 2. How many Units does it take to produce 100 square meals?    

Part 3. How many square meals can be produced with 20 units of unmentionable?    

Part 4. If the input costs 6 per unit, what is the average cost (AC) of producing 36 square meals?    

Part 5. If the input costs 6 per unit, what is the average cost (AC) of producing 216 square meals?    

Part 6. The total cost function is rising at an Increasing, Decreasing/Diminishing or Constant rate?   

Answer 1

1)

SM = U2

In order to check for returns to scale, multiply the variable U by a factor t

SM’ = (tU)2

SM’ = t2U2

SM’ = t2SM

Since SM’ > tSM, it means there are increasing returns to scale

2)

100 = U2

Taking square root both sides,

U = 10

3)

SM = U2

SM = 20.20

SM = 400

4)

36 = U2

Taking square root both sides,

U = 6

AC = TC/Q = (6x6)/36 = $1

5)

216 = U2

Taking square root both sides,

U = 14.7

AC = TC/Q = (6x14.7)/216 = $0.408

6)

TC is decreasing