per unit. The total cos incurred consists of a fixed overhead of 28 dollars plus production cost of 2 dollars per unit of x. i Write down the monopolist's profit as a function of x (2 Marks) ii Find the maximum profit realized by the monopolist in producing x units of the commodity (2 Marks)

To find the monopolist's profit as a function of x, we need to consider the total revenue and total cost.<br /><br />Total Revenue (TR) = Price per unit * Quantity sold<br />Total Cost (TC) = Fixed Cost + (Production Cost per unit * Quantity produced)<br /><br />Given that the price per unit is $10, the fixed cost is $28, and the production cost per unit is $2, we can write the profit function as:<br /><br />Profit = Total Revenue - Total Cost<br />Profit = ($10 * x) - (28 + 2x)<br />Profit = 10x - 28 - 2x<br />Profit = 8x - 28<br /><br />So, the monopolist's profit as a function of x is:<br /><br />Profit = 8x - 28<br /><br />To find the maximum profit realized by the monopolist in producing x units of the commodity, we need to find the value of x that maximizes the profit function.<br /><br />To do this, we can take the derivative of the profit function with respect to x and set it equal to zero:<br /><br />d(P) / dx = 8<br /><br />Setting the derivative equal to zero and solving for x:<br /><br />8 = 0<br /><br />This equation has no solution, which means that the profit function is a linear function and does not have a maximum value. The profit will continue to increase as the quantity produced increases.<br /><br />Therefore, there is no maximum profit realized by the monopolist in producing x units of the commodity.