$1-$Consider a monopolist operating in a market where the demand curve is linear and downward sloping. The monopolist's marginal cost is constant across all levels of output.

a$.$ Graphically represent the demand $($D$),$ marginal revenue $($MR$),$ and marginal cost $($MC$)$ curves on a single graph. Label your axes appropriately.

b$.$ Determine the monopolist's profit$-$maximizing output level and price. Mark these on your graph.

c$.$ Highlight consumer surplus, producer surplus and deadweight loss associated with profit$-$maximizing quantity and price.

d$.$ Why am I not asking for a supply curve?

$2.$ Consider a market best suited for a natural monopoly due to substantial economies of scale. The demand curve for the product is linear and downward sloping. The natural monopolist experiences decreasing average costs $($AC$)$ over a significant range of outputs, represented by a downward sloping AC curve. Marginal cost $($MC$)$ is below AC and constant across all levels of output.

a$.$ Graphically represent the demand $($D$),$ average cost $($AC$),$ marginal revenue $($MR$)$ and marginal cost $($MC$)$ curves on a single graph. Label your axes clearly.

b$.$ Determine the monopolist's profit$-$maximizing output level and price using the intersection of MC and MR$.$ Mark these on your graph.

c$.$ Highlight consumer surplus, producer surplus and deadweight loss associated with profit$-$maximizing quantity and price.

d$.$ Now, imagine a regulatory body imposes a "fair return" price, allowing the natural monopoly only to break even $($Price $=$ AC$)$ and that the monopolist provide a quantity at that price such that there is no surplus or shortage $($quantity supplied$=$quantity demanded at that price$).$ Identify this price and the corresponding output level.

e$.$ Is the output level from d$.$ efficient? Why or why not?

$3.$ Consider a firm operating in a market where it has some degree of market power, enabling it to set prices rather than being a price taker. The firm realizes that the consumers in its market have varying price elasticities of demand based on their individual characteristics. Assume constant marginal costs for simplicity.

a$.$ Assume that the firm identifies two distinct segments in its market: Segment A$,$ with a relatively inelastic demand, and Segment B$,$ with a more elastic demand. Draw and label the demand curves for each segment. It might be easiest to do this on two separate graphs, but you can put these on one graph if they are clearly labeled.

b$.$ If the firm practices third$-$degree price discrimination:

What prices will it charge in each segment to maximize its total profit?

Identify and shade the consumer surplus and producer surplus for each segment.

c$.$ Now assume that the firm has perfect information about all consumers and can charge them their marginal value for each unit sold $($that is$,$ they can charge separately both to different consumers and to the same consumer for subsequent units$).$ Assume constant marginal costs. Draw the demand curve in this market, the price schedule the monopolist will follow, and identify consumer, producer surpluses and deadweight loss, if any.