91Ó°ÊÓ

The total cost, average and marginal cost for firm1 is calculated below:

$$\begin{gathered} {\text{TC}}_{\text{1}}{\text{= 20 + 5Q}}_{\text{1}}^{\text{2}} \\ {\text{TC}}_{\text{Q = 0}}\text{= 20 + 5}{\left(\text{0}\right)}^{\text{2}} \\ \text{= 20} \\ {\text{AC}}_{Q=0}\text{=}\frac{\text{TC}}{\text{Q}} \\ \text{=}\frac{\text{20}}{\text{0}} \\ \text{= -} \\ {\text{MC}}_{Q=0}{\text{= TC}}_{\text{n}}{\text{- TC}}_{\text{n - 1}} \\ \text{= -} \\ {\text{TC}}_{\text{Q = 1}}\text{= 20 + 5}{\left(\text{1}\right)}^{\text{2}} \\ \text{= 20 + 5} \\ \text{= 25} \\ \text{AC =}\frac{\text{TC}}{\text{Q}} \\ \text{=}\frac{\text{25}}{\text{1}} \\ \text{= 25} \\ {\text{MC = TC}}_{\text{n}}{\text{- TC}}_{\text{n - 1}} \\ \text{= 25 - 20} \\ \text{= 5} \end{gathered}$$

Similarly, the total, average, and marginal costs are calculated from 0 to 5 units.

The table below shows the total cost, average cost, and marginal cost of all 4 firms.

The cartel will assign the production in such a manner that the lowest marginal cost is achieved:

Thus, firms 1 and 4 will produce 2 units each, and firms 2 and 3 will produce 3 units each.

The firm whose marginal cost is lowest beyond its allocation has an incentive to cheat. Thus, firm 2 has the lowest marginal cost for producing the 4^thunit than the other; also, marginal cost is lower than the price; hence, firm 2 has an incentive to cheat. The other firm has marginal cost either greater than or equal to price. Firms 3 and 4 have marginal costs greater than the price; thus, there is no incentive to cheat. Firm 1 is indifferent as its marginal cost is less than the price.