Can someone please help with this Public goods and free ridinghomework problem? Thank you in advance!!

The cost of building a park is C(g) = 10g², where g is size of a park in square miles. Total benefits from the park for each individual is: B = 3g 2g² . There are 10 identical individuals in the community. In class, we showed that under voluntary contribution, it will not be an equilibrium for the 10 people to provide the efficient amount of the public good (because of free riding). In this problem, we are going to walk you through steps to find what is the equilibrium level of contribution.

1. To show that everyone contributing 0 is not an equilibrium, suppose that 9 people were contributing 0. How much would the last person contribute (in dollars, not units of the good)?

To find an equilibrium where everyone is donating the same amount, let's introduce some notation: let g1 be the amount of park that person 1 provides. Notethat the cost of providing this amount of park will depend on the quantity in equilibrium. It is easiest to describe contributions in terms of units of the good. Let G₁ = g2 + g3 + + g10 be the combined contribution of everyone else. Thus, by construction, we have g = g₁ + G₁. In a voluntary provision equilibrium, we want to consider how person 1 will choose their level of provision, taking as given the amount that others are giving. That is, we want to figure out the optimal g₁ as a function of _G1, which is taken as fixed by person 1. (For those of you who know the term, we are finding a Nash Equilibrium.)

2.Person 1 will choose g₁ taking into account their own benefits, but ignoring everyone else's. Write down the marginal benefit function that they use to make decisions, and substitute our definition of g = g₁ + G₁ so you have marginal benefits as a function of g₁ (which is a choice) and G₁, which person 1 takes as fixed. Write down the relevant marginal cost curve as well, using the g1 and G₁ notation.

3.We are going to find the symmetric equilibrium, where all 10 people make identical contributions. Symmetric contribution implies something about the relationship between g1 and G₁. Specifically, G₁ = g₁. What is ?

4.If you set the marginal benefit equal to the marginal cost (which defines the optimal g₁) from question 2, and you use the equation from question 3, you should be able to solve for the equilibrium quantity. What is the total amount of the public good provided in the symmetric voluntary contribution equilibrium? (That is, what is g (rather than g₁)? Round your answer to 3 digits.)