Answer to Question #227378 in Economics of Enterprise for abel

Question #227378

Suppose the cost function is given as C = 135 + 75Q – 15Q2 + Q3. Prepare a cost schedule (table) showing the TFC, TVC, TC, AFC, AVC, MC, and ATC. Is this cost function a short run or a long run cost function? Why? Draw the cost curves on the basis of cost data obtained from the cost function



1
Expert's answer
2021-08-20T11:20:12-0400

TFC"=" production which is not variable during short run. It remains fixed.

TFC"=" TC"-" TVC

"=" 135

TVC "=" cost that is variable. It changes with change in the quantity produced or change in output.

TVC"=" TC"-" TFC

"=" 75Q"-" 15Q"^{2}" "+" Q"^{3}"

TC"=" is total cost that is related to production.

"=" 135 "+" 75Q "-" 15Q"^{2}" "+" Q"^{3}"

AFC "=" "\\frac{TFC}{Q}" It changes with change in quantity as the output changes but the fixed cost remains the same.

"=" "\\frac{135}{Q}"

AVC "=" "\\frac{TVC}{Q}" It is the average of total variable cist and is U_shaped.

"(" 75"-" 15Q "+" Q"^{3}" "\/" Q

"=" 75"-" Q "+" Q"^{2}"

MC "=" is additional cist incurred due to producing one extra unit of a product MC "=" TC"_n" "-" TC"_{n-1}"

"=" 75 "-" 30Q "+" 3Q"^2"

ATC "=" is defined as to ta cost divided by total quantity.

ATC"=" "\\frac{TC}{Q}" Or AVC "+" AFC

"=" "(" 135 "+" 75Q "-" 15Q"^2" "+" Q"^{3}" ")" "\/" Q

"=" 135 "+" 75 "-" 15Q "+" Q"^2"

Cost curves on the basis of cost data obtained from the cost function.

A short run cost function because there is some quantity of an input which remains fixed.



The cost curve will show a U shaped average cost and a sloping marginal cost as shown above


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