There are competitive firms that produce yogurt according to the supply function y=K+L. the prices of K and L are r and w, respectively. there are a hundred identical consumers who each have an income of $1000, and who consume yogurt and xenon. their preferences are summarized in the utility function u=x^0.5y^0.5. this implies that marginal utility of X= 0.5x^-0.5y^0.5and marginal utility of Y=0.5x^0.5y^-0.5. because xenon is produced through a process with constant returns to scale, its price is constant, and we will assume it equals $1, and denote the price of Y by "P"

1. the government imposes a tax on L so that for every unit of L used, firms must pay a tax of 3, as well as the wage of 5. how do I find the long-run price and total quantity consumed of yogurt? and how much does the government earn because of it??
2. the government was so pleased with the tax that it increased the tax to 7. what's the new long run price and total quantity consumed of yogurt and how much does the government earn now?