Question

Two dairy farmers produce milk for a local town with local milk demand given by P = 300 - 3Q (P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC = 150 + 2Q (where denotes output).

(a) Suppose that both farmers decide to form a cartel, determine profits for each farmer under the cartel     

(b) What output should farmer 1 produce if he/she expects their rival to produce 20 units?  

Answer 1

$TR = P×Q$

$TR = (300-3Q)Q$

$TR = 300Q -3Q^2$

$MR = \frac{dTR}{dQ}$

$MR = 300-6Q$

$MC = \frac{dTC}{dQ}$

$MC = 0 + 2$

$= 2$

$MC = MR$

$2 = 300-6Q$

$6Q = 300 - 2$

$Q = 298/6$

$Q = 49.67$

$P = 300 -3(49.67)$

$P = 150.99$

$= \frac{150.99}{2}$

$Profit for each = 75.495$