Two businesses contribute to maintaining green spaces. Every year the companies 1 and 2 decide how much to contribute, where the joint contribution is x= x1 + x2 The spaces Greens are common so there is no rivalry. The market rents of each company depend on the quality of its infrastructure and green spaces. The utility function of firm 1 is: Z1 = Z1 + ln(x1+x2)-x1 The utility function of firm 2 is: Z2 = Z2 + 2 ln (x1+x2) - x2 Where Z1 and Z2 are constants (a)Find the best response of firm 1 based on the contribution of firm 2, R1(X2) for all x2 [0,oo) (b) Find the best response of firm 2 based on the contribution of firm 1, R2(X1) for all x1 [0,oo) (c) Find the Nash equilibrium (x1, x2) and the total contribution x = x1 + x2. (d) Is there free riding in this equilibrium? From which company? explain. (e) Determine the total Pareto efficient input level. How does it compare to the results? found in (c)? explain
Two businesses contribute to maintaining green spaces. Every year the companies 1 and 2 decide how much to contribute, where the joint contribution is x= x1 + x2 The spaces Greens are common so there is no rivalry. The market rents of each company depend on the quality of its infrastructure and green spaces. The utility function of firm 1 is:
Z1 = Z1 + ln(x1+x2)-x1
The utility function of firm 2 is:
Z2 = Z2 + 2 ln (x1+x2) - x2
Where Z1 and Z2 are constants
(a)Find the best response of firm 1 based on the contribution of firm 2, R1(X2) for all x2 [0,oo)
(b) Find the best response of firm 2 based on the contribution of firm 1, R2(X1) for all x1 [0,oo)
(c) Find the Nash equilibrium (x1, x2) and the total contribution x = x1 + x2.
(d) Is there free riding in this equilibrium? From which company? explain.
(e) Determine the total Pareto efficient input level. How does it compare to the results? found in (c)? explain
Question b
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