Consider a two-firm model with a negative production externality. Let xi denote firm i’s output, with i = 1, 2. Suppose that two firms operate in two different competitive markets and each firm sells its product in its respective competitive market, at the prices p1 = 100 and p2 = 150, respectively, and that they face the same direct production cost ci (xi ) = xi2 /2. Let e(x1 , x2 ) = x1 x2 be the external cost on firm 2’s activity  generated by the production of firm 1. Find each firm’s best response function to the output set by the other firm and compute the Nash equilibrium assuming that firms choose their output non-cooperatively and independently. Illustrate the equilibrium in an appropriate graph.  Calculate each firm’s equilibrium profits and the total external cost imposed on firm 2.

Consider a two-firm model with a negative production externality. Let x_i denote firm i’s output, with i = 1, 2. Suppose that two firms operate in two different competitive markets and each firm sells its product in its respective competitive market, at the prices p₁ = 100 and p₂ = 150, respectively, and that they face the same direct

production cost c_i (x_i ) = x_i² /2. Let e(x₁ , x₂ ) = x₁ x₂ be the external cost on firm 2’s activity 

generated by the production of firm 1.

1. Find each firm’s best response function to the output set by the other firm

   and compute the Nash equilibrium assuming that firms choose their output non-cooperatively and independently. Illustrate the equilibrium in an appropriate graph. 

2. Calculate each firm’s equilibrium profits and the total external cost imposed on firm 2. 

3. c. Rational choice theory assumes that economic agents are rational and self-interested. Based on the evidence from behavioural laboratory experiments (e.g., dictator games), behavioural economists suggest that people are not always self-interested, rather they have intrinsic preferences for others’ well-being (e.g., altruism, inequity aversion). However, some other studies in behavioural economics investigate this further and disentangle the intrinsic preferences into several other factors. Following the discussion in the lecture, state two such studies that try to disentangle the true intrinsic preferences based on dictator games in the lab. Explain clearly and briefly the following: (i) what each study addresses; (ii) brief description of the experimental design; and (iii) intuitive explanations.