Please show all work and calculations.
Consider a monopoly firm facing market demand expressed as p = 200 - ½y , where the firm's total cost in dollars per month is: TC = 2y2 + 15y + 144, where p is measured in dollars per unit and y is measured in units per month.
a. Write the expressions for the firm's Total Revenue, Marginal Revenue, Average Cost and Marginal Cost.
b. Show on a graph, supported by calculations, what quantity this monopolist will produce each period to maximize profits. Your graph should also show (and label) the demand curve, marginal revenue curve and marginal cost curve. Report the firm's optimal price per unit.
c. Calculate, and label as point A on your graph, the value of average cost at the optimal output level.
d. Calculate the firm's profit per month and show it as a shaded area on your graph.
e. What is the value of the own-price elasticity of demand at the profit maximizing quantity?
The value of the own-price elasticity of demand is derived.