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 625 square meals? ____________

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

Part 4. If the input costs 5 per unit, what is the average cost (AC) of producing 25 square meals? ____________

Part 5. If the input costs 5 per unit, what is the average cost (AC) of producing 125 square meals? ____________

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

Answer 1

Given,

Part 1: Let us assume the input changes by a factor of lambda

From above equation we can see the Input changed by a factor of , while the output changed by a factor of . Hence, the given production function exhibits Increasing returns to scale.

Part 2: When Output is 625

Part 3: When U = 20

Part 4: When Input Cost = $ 5,

Cost of producing 25 meals

For producing 25 Square meals we require 5 U.

Total cost of producing 25 square meals = 5 * 5 = $ 25

Average cost of producing 25 SM = 25/25 = $ 1 per square meal

Part 5: When input cost = $ 5

Output = 125 square meals

Cost of producing 125 square meals =

Average cost of producing 125 square meals

Average Cost = $ 0.45 per Square meal.

Part 6: As we can see from the previous two cases the Average Cost decreased with the increase in total output. Therefore, total cost function is decreasing or diminishing.

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