52.There is an industry controlled by a monopolist that is not regulated so the Monopolist will maximize profits with no interference.Recall the Marginal Revenue of any firm with "market power" is the change in total revenue as quantity changes, which could lead to the "arc approach" of calculating MR.Also recall the marginal revenue is the slope of the total revenue curve as quantity of output changes, which leads to the "point slope approach".For mathematical reasons, when trying to determine the optimal quantity to maximize profits, the slope approach is easiest to use.In notation from lecture notes #8 the slope approach can be written:MR = TR / Q = P + Q P / Q with P / Q being the slope of the demand curve.If the demand curve is estimated by a simple linear function of the form Q_D = a + b P with b < 0, then recall the slope of the demand curve is 1 / b.Substituting, MR = P + Q / b.To get the MR to a function of only Q, the P needs to be eliminated.Convert the demand curve into an "inverted demand curve" to get P = [Q - a] / b then substitute the right side into the MR equation to get MR = [[Q - a] / b] + [Q / b].Rearrange and simplify to get MR = [2Q/b] - [a/b].After analyzing industry daily demand and conducting some experiments, "a" is estimated to equal 49 and b equals -1.4.

The monopolist estimates its daily marginal cost function to be MC = x + y Q with x = 2.4 and y = 0.9.How many units should the monopolist produce to maximize its profits or producer's surplus?Note that once you have the optimal Q, it can be proven by plugging the Q into both the MR and MC curves.Please round to 2 decimals, for example 37.15 or 52.82.

Quantity:

53.What price would the monopolist charge consumers for each unit it produces?Please round to one cent, for example $12.36 or $41.55.

Price:

54.At the monopolist's optimal quantity and price, how much revenue is it collecting?Please round to one cent, for example $459.17 or $194.53.

Spending and Revenue:

55.At the monopolist's optimal quantity and price, what is the "producer's surplus"?Please round to one cent, for example $29.32 or $71.31.There are several approaches to estimate the producer's surplus.One is to estimate the area.The second is to estimate "Total Costs" and then deduct it from revenue.Another is to calculate Average Cost per unit and then deduct it from price to get profit per unit and then multiply by the optimal Q.All 3 methods should give the same result.

Producer's Surplus:

56.At the monopolist's optimal quantity and price, what is the "consumer's surplus"?Please round to one cent, for example $8.55 or $17.73.

Consumers' Surplus: