Question

Shut down point is where AR=AVC AR is given as 500 Given TC= 5500+5Q2 means TFC= 5500 and TVC= 5Q2 (because TC=TFC+TVC and TFC is constant in the short run) This means AVC=TVC/Q= 5Q Shut down point will be whree 5Q=500 i.e. where Q=100 ii) profit = TR-TC= (AR*Q)-TC= 500Q- 5500-5Q2 for profit maximisation level of the first order derivative must be equated to zero and the second order derivative must be less than 0 First order derivative of profit function is 500-10Q equating it to zero we get Q=50 Second order derivative of the profit function is -10 which is less than zero so we can say that profit is maximised by the firm at Q= 50 units At Q=100 only the AVC is covered which means there is a loss to the extent of the AFC. So the firm should cut down production to 50 units so as to maximise its profit.. briefly explain the connection between total product, average product and marginal product for a firm operating with one variable input ..With an appropriate diagram/s

Answer 1

Relationship between TP, AP and MP assuming one variable of input :

1) Initially TP increases at an increasing rate, MP also increases. As long as MP is more than AP, AP rises as shown in the above diagram.

2) When TP increases at an diminishing rate, MP decreases and become equals to AP.

3) When MP is equal to AP, AP is at its maximum. When MP is less than AP, AP falls. Thereafter, both MP and AP fall

4) When TP reaches its maximum point, MP becomes zero.

5) Thereafter, When TP starts decreasing, both AP and MP starts falling but MP becomes negative, whereas AP remains positive. MP falls at a faster rate in comparison to fall in AP.