Consider a Salop circular model. Assume that firms' cost functions are \( C(q) = 0.25 \) (with zero marginal costs). Assume that consumers incur transportation costs which are linear in the distance travelled; specifically, a consumer incurs transportation costs of \( 2|d| \) from travelling a distance \( d \). A consumer buys only one unit of the product and derives 5 units of utility from consuming it.

The firms engage in a two-stage game: they choose whether to enter in the first stage, and prices in the second stage. Assume that each of the \( N \) firms who decide to enter the market locate in equidistant fashion along the circular city.

(a) Solve for the equilibrium price, assuming \( N \) firms are in the market.

(b) Given this, solve for the number of firms who would have entered the market, assuming that firms enter only when they foresee that they will be able to recoup their fixed costs from doing so.

(c) Solve for the number of firms which would minimize aggregate transportation costs in the economy.

(d) Solve for the number of firms which would minimize the sum of (aggregate transportation costs + total fixed costs) in the economy.

Answer all the question for me