Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively.
(a) Express his marginal rate of substitution (MRS) between goods X and Y. As the amount of X increases relative to the amount of Y along the same indifference curve, does the MRS increase or decrease? Explain.
(b) What is his optimal consumption bundle (X*, Y*), given income and prices of the two goods?
(c) How will this bundle change when all prices double and income is held constant?  When all prices double AND income doubles?
(d) Derive the demand curve for good X and demand curve for good Y.
Now a government subsidy program lowers the price of X from $20 per unit to $10 per unit.
(e) Calculate and graphically show the change in good X consumption resulting from the program.
(f) Graphically show the change in consumption attributable to the separate income and substitution effects.
(g) Show (graphically) how much the program cost the government.