8. A consumer has utility function "(x, y) = vry. for two goods, X and Y, where c is some positive constant. Here, or > 0 denotes the amount of X consumed and y > ( the amount of Y' consumed. Each unit of X costs I dollar and each unit of Y costs I dollar, and the consumer has a budget for X and Y of M dollars. Use the Lagrange multiplier method to find the quantities a" of X and y' of Y the consumer will consume in order to maximise his utility subject to the budget constraint. (Your answers will depend on c and M.) Find the corresponding value, A', of the Lagrange multiplier. Suppose that V - u(x'. y') is the maximum achievable utility. Find an explicit expression for V in terms of c and M, and OV verify that OM