Rubber for erasers is produced in the market. There are equations for the Supply and Inverse Demand of eraser rubber that model its Supply and Demand graph. These equations are (for supply), P = 20 + Q^s, and (for Inverse Demand), P = 80 - Q^d. With that said, the government realizes that it is not turning out enough revenue from the market. As a result, it places a per-unit sales tax of $10.

(Part I) Draw the market equilibrium with the government intervention (Q**, P_D**, and P_S**) of the sales tax. Please label the graph for slopes, equilibrium points, sales tax, etc.

(Part II) What is the market equilibrium without the intervention of the government?

(Part III) The government once again realizes that the previous tax was not sufficient, and the government is still not making enough money. So, it increases the sales from $10 to $20. Consequently, what is the new market equilibrium point (Q**, P_D**, and P_S**) with this new intervention? It is not necessary to label this point on the graph.

(Part IV) What is the effect of the change in the sales tax on the government's surplus (GS**)? Essentially, please determine GS** before the change in the tax and after the change in the tax.