Firm A operates in competitive markets. It uses a single input x to produce the output y. The technology of this firm can be described in the following the production function: y = x2 for x between 0 and 3 and y = 2x + 3 for x greater than 3. The price of the output y is $2 and the price of the input x is $5. Derive the marginal product MPx of the input x. (Hint: you need to discuss different values of x.) Write down firm A's profit function. Given the prices of input and output, what is the profit-maximizing amount of input and what is the profit-maximizing amount of output? Draw a graph of the production function and isoprofit lines to illustrate this optimum. How much profit does firm A make at the optimum? Now suppose that the price of the output y has decreased to $1. And the price of the input x is still $5. Write down firm A's profit function. Given the new prices of input and output, what is the profit- maximizing amount of input and what is the profitmaximizing amount of output? Draw a graph of the production function and isoprofit lines to illustrate this optimum. How much profit does firm A make at the optimum