Two firms are operating in the market for domestic robots: 'Elonbot' and 'Schitted', denoted respectively by subscripts _E and _S. Assume that both firms are the only two producers in this market.

_total= _E+_S

These two firms are facing a demand function equal to_D= 800 0.5

These two firms have different total cost functions, as shown below, because each plant is slightly different.

T_E= 40 + 2²

TC_S = 15+22

1. Calculate the marginal revenue and marginal cost functions for each firm. (Hint: you need to firstly convert the demand function into its inverse form. Also this is a Cournot oligopoly.)

1. Calculate how much each firm should be producing to maximise its profits.

1. Calculate the price at which the firms are maximising profits.