Johannes has a utility function given by U=xy/(x+y) where x is the amount of product 1 consumed per period and y is the amount of product 2 consumed per period. Johannes’ monthly income is $200.
if the first 50 units of product 1 sell for $2 per unit but for x>50 the price of product 1 falls to $1 per unit. Assume Johannes can buy as much of product 2 as he likes at a constant price of $2 per unit.
Find Johannes’ utility maximizing consumption levels for products 1 and 2 . Illustrate your answer with a diagram showing Johannes’ budget line and his highest attainable indifference curve.