I have a difficulty in finding the equilibrium vector of this Markov system.

2 DUE 28 NOVEMBER 2019 Shrimp Corn Buildings Energy Goods/services produced Fisheries 0.25 0.20 0.10 0.20 0.20 Corn Farmers 0.17 0.27 0.22 0.21 0.15 Construction 0.22 0.26 0.21 0.14 0.25 Oil 0.18 0.17 0.27 0.35 0.25 Goods/services 0.18 0.10 0.20 0.10 0.15 Notice that each column adds to one, meaning that all the production is consumed. PF PW Now, let p = Pc be the prices (see Lay 1.6) (in $) of the fisheries, corn farmers, construction, oil and goods/services po PG sectors, respectively. For example, pp is the total income of the fisheries as well as the cost of all the shrimp. If the fisheries produces $100 worth of shrimp, then the income of the fisheries will also be $100 since all of the shrimp are bought one way or the other and all that income goes to the fishing sector. Since the economy is closed, we must have Lp = p where L is the matrix describing the distribution of products (essentially, the table above). The system of equations Lp = p can be rewritten as (L - D)p = 0 and solved. (a) Assume the total value of all shrimp produced is $100. Solve Lp = p to find the equilibrium prices for each sector in order that the island economy is balanced. Then store the equilibrium vector of prices as vecprice. Hint: This can be done through solving a linear system, or computing an eigenvector. Second hint: The command sum(A) returns the column-sums of a matrix. You can use this to check that you have entered the matrix correctly