1a) Egon consumes two goods X and Y. Egon’s utility function is UE = X^0.25Y^0.5. The price of X is $10, and the price of Y is $5. Egon has $300 to spend this month.

Egon's Marginal Rate of Substitution is:

1b) Egon consumes two goods X and Y. Egon’s utility function is UE = X^0.25Y^0.5 . The price of X is $10, and the price of Y is $5. Egon has $300 to spend this month. Egon is currently consuming X =20, Y = 20.

Egon's current consumption is not optimal. Use the MRS and the prices to suggest a shift in consumption that will increase Egon’s utility. You must use a slopes-based argument here for full credit, and follow the templates for discussing a "slopes trade."

1c) Egon consumes two goods X and Y. Egon’s utility function is UE = X^0.25Y^0.5 . The price of X is $10, and the price of Y is $5. Egon has $300 to spend this month. Egon is currently consuming X =20, Y = 20.

Egon’s colleague Ray also consumes X and Y. At Ray’s current bundle, Ray’s MRS= -1. Using their MRS at these bundles (i.e. Egon’s at X=20, Y=20), propose a mutually beneficial trade. Demonstrate both are better off after this trade. Be specific: Ray gives ___ to Egon; Egon gives ___ to Ray. Remember prices don’t matter here.

1d) Egon consumes two goods X and Y. Egon’s utility function is UE = X^0.25Y^0.5 . The price of X is $10, and the price of Y is $5. Egon has $300 to spend this month. Egon is currently consuming X =20, Y = 20.

Solve for Egon's optimal bundle. In your written work, include a graph of indifference curves and budget constraint that shows Egon's original X=Y=20 bundle and his new optimal bundle. Note that Ray is no longer relevant.