Consider a consumer with the utility function u(x,y) =x^1/2 + y. Suppose the cost of

producing good x is given by the cost function c(x) and the price of good y is $1.

Illustrate that the solution to the social planner's problem in terms of production of x

is equivalent to the perfectly competitive market outcome. (You may assume that the

consumer is endowed with an income of M > 0).