MUx MUy (1) = Px Py (2) PxX + pyY = I Steps: 1. You will be given the marginal utilities, the prices, and income. Put the marginal utilities and prices into equation (1). Simplify and solve for either X (as a function of Y) or Y (as a function of X). 2. Take your solution from step 1 and substitute it into equation (2). You now have only one unknown. Solve for it. 3. Take your solution from step 2 and substitute it back into your solution from step 1. Solve for the second unknown. In each of the following practice problems, find the optimal combination of X and Y. 1. Utility: U = X0.5y0.5 Marginal Utilities: MUx = 0.5 (Y) 0.5 MUY = 0.5 () 0.5 Income and Prices: I = 1,000 Px = 5 Py = 5 Answer: X = 100; Y = 100 2. Utility: U = X0.6y0.4 Marginal Utilities: MUx = 0.6 (*) MUY = 0.4 () 0.6 Income and Prices: I = 600 Px = 2 Py = 4 Answer: X = 180; Y = 60 3. Utility: U = X0.30.7 Marginal Utilities: MUx = 0.3 () 0.7 MUY = 0.7 () Income and Prices: I = 2,100 Px = 30 Py = 6 Answer: X - 21; Y = 245