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
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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