Part a) The Cob Douglas production function is given as:
To show that this function is homogeneous with degree 3, we introduce be a parameter, t.
Using properties of exponents, we on tinder:
This implies that:
Simplify the exponent of t to get;
Hence the function is homogeneous with degree, 3
Part b) To verify Euler's Theorem, we must show that:
Verifying from the left:
Q•E•D
Answer:
$633,000.
Explanation:
We use the High-low method to get the cost formula:
This means 5,000 machine hours generate 140,000 labor cost
We divide and get the variable cost generate per machine hour:
Cost 140000
machine hours 5000
140,000/5,000 = 28
variable cost 28
Next, we use this to calculate the fixed cost:
total cost = variable cost + fixed cost
fixed cost = total cost - 28 X DL
<u>High:</u>
Total Cost 710,000
Variable 399,000 (14,250 x 28)
Fixed Cost 311,000
<u>Low:</u>
Total Cost 570,000
Variable 259,000 (9,250 x 28)
Fixed Cost 311,000
Now with the cost formula we solve for 11,500 machine hours
cost = 311,000 + 28 X Machine Hours
cost = 311,000 + 28 x 11,500
cost = 633,000