Question

4. Determine the average function and the marginal function for each of the following functions
Totals:
a) Total income TR = 100 Q - Q²
b) Total cost TC = 1000+ 10 Q + .01 Q²
c) Total profit TP = 50 Q - 0.1 Q2 - 1000

5. Given the following total income function TR = 100 Q - Q², determine the level of production that allow to maximize total income.

6. Given the total cost function TC = 200Q - Q² + 0.3 Q³, determine the level of production that minimize the average total cost.

Graphically complement the answers to questions 5 and 6.

Answer 1

4. (a) Total income : TR= 100Q - Q2

Average income : TR/Q = (100Q-Q2)/Q = 100- Q

Marginal income : dTR/dQ = 100- 2Q

(b) Total cost : TC = 1000+ 10Q +0.01Q2

Average cost : TC/Q = 1000/Q + 10 + 0.01Q

Marginal cost : dTC/dQ = 10 + 0.02Q

(c) Total profit : TP = 50Q -0.1Q2 -1000

Average profit : TP/Q = 50 - 0.1Q

Marginal profit : dTP/dQ = 50- 0.2Q