Question

Assume the short run variable cost function for Japanese beer is VC=0.5q^0.67

If the fixed cost​ (F) is $1500 and the firm produces 600​units, determine the total cost of production​ (C), the variable cost of production​ (VC), the marginal cost of production​ (MC), the average fixed cost of production​ (AFC), and the average variable cost of production​ (AVC). What happens to these costs if the firm increases its output to 650?

Assuming the firm produces 600 units, the variable cost of production​ (VC) is

VC=???????. ​ (Enter your response rounded to two decimal​places.)

The total cost of production​ (C) is C=$????.?? ​(Enter your response rounded to two decimal​ places.)

The marginal cost of production​ (MC) is MC=​$?.?? ​(Enter your response rounded to two decimal​ places.)

The average fixed cost of production​ (AFC) is AFC=​$?.??   ​(Enter your response rounded to two decimal​ places.)

The average variable cost of production​ (AVC) is AVC=​$?.??​(Enter your response rounded to two decimal​ places.)

Now suppose the firm increases output to 750 units.

The variable cost of production​ (VC) is VC=​$???.?? ​(Enter your response rounded to two decimal​ places.)

The total cost of production​ (C) is C=​$????.?? ​(Enter your response rounded to two decimal​ places.)

The marginal cost of production​ (MC) is MC= $?.??  ​(Enter your response rounded to two decimal​ places.)

The average fixed cost of production​ (AFC) is AFC=​$?.??     ​(Enter your response rounded to two decimal​ places.)

The average variable cost of production​ (AVC) is AVC=​$?.??   ​(Enter your response rounded to two decimal​places.)

Answer 1

Answer
Assuming the firm produces 600 units, the variable cost of production​ (VC) is

VC=0.5q^0.67
=0.5*600^(0.67)
=36.3355168
=36.34

The total cost of production​ (C) is

C=FC+VC=1500+36.3355168=1536.34

The marginal cost of production​ (MC) is

MC=dVC/dq=0.5*(0.67)q^(0.67-1)=0.5*(0.67)q^(-0.33)
=0.5*(0.67)*600^(-0.33)=0.0405746605
MC=0.04

The average fixed cost of production​ (AFC) is AFC
AFC=FC/Q=1500/600=2.50

The average variable cost of production​ (AVC) is AVC

AVC=VC/q=(0.5q^0.67)/q=(0.5*(600)^0.67)/600=0.0605591947
=0.06

Now suppose the firm increases output to 750 units.

the variable cost of production​ (VC) is

VC=0.5q^0.67
=0.5*750^(0.67)
=42.1950058=42.20

The total cost of production​ (C) is

C=FC+VC=1500+42.1950058=1542.20

The marginal cost of production​ (MC) is

MC=dVC/dq=0.5*(0.67)q^(0.67-1)=0.5*(0.67)q^(-0.33)
=0.5*(0.67)*750^(-0.33)=0.0376942052
MC=0.04

The average fixed cost of production​ (AFC) is AFC
AFC=FC/Q=1500/750=2.00

The average variable cost of production​ (AVC) is AVC

AVC=VC/q=42.1950058/750
=0.0562600077
=0.06