The residents of Hockeytown have $10 million to distribute

The residents of Hockeytown have $10 million to distribute between public schools (K-12 education) and private goods. Each unit of public schools costs $1 million.

(i) Graph Hockeytown’s budget constraint, making sure to label axis.

(ii) Suppose Hockeytown decides to build 5 schools. Draw the equilibrium, making sure you include the indifference curve.

Suppose the Federal government chooses to subsidize public schools in Hockeytown to enhance access to education. Specifically, the Federal government will cover the expenses of building an additional public school for every two public schools financed by Hockeytown (buy 2, get 1 free). That is, any Federal funding will be earmarked to public schooling.

(iii) Draw the new budget constraint.

(iv) Will Hockeytown construct more or fewer units of public schools? Will it purchase more or fewer private goods? Answer by illustrating the new equilibrium with the graph and explain.

Please provide detailed answers.