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- 15Q2^{2} ++ Q3^{3}

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

== 135 ++ 75Q - 15Q2^{2} ++ Q3^{3}

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

== 135Q\frac{135}{Q}

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

(( 75- 15Q ++ Q3^{3} // Q

== 75- Q ++ Q2^{2}

MC == is additional cist incurred due to producing one extra unit of a product MC == TCn_n - TCn1_{n-1}

== 75 - 30Q ++ 3Q2^2

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

ATC== TCQ\frac{TC}{Q} Or AVC ++ AFC

== (( 135 ++ 75Q - 15Q2^2 ++ Q3^{3} )) // Q

== 135 ++ 75 - 15Q ++ Q2^2

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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