How to graph a monopoly that does not exhibit the properties of a contestable market? This question is not a homework question. I am taking a course in industrial organization, and the textbook/professor have given an illustration of a monopoly that is a contestable market. However, I am having trouble seeing, graphically, how an illustration of a non-contestable monopolistic market would look. 

The properties of contestable markets are:

(i) Free entry, (ii) Absolute entry, (iii) No sunk costs with entry. 

I have included the image used in both the textbook, and by the professor for contrasting purposes. One other question, if LRAC is decreasing as output increases, would that mean that the monopolist is facing economies of scale, which would cause there to be a barrier for the entrant?

Thank you in advance!
The diagram above describes a Natural Monopoly. These economies have the characteristic that the long run average costs are decreasing (and hence the LRMC is below the LRAC curve). That is, costs reduce as the firm keeps producing more. *Firms with network effects (e.g. telecom industry) is an example of such an industry.

Lets look at 2 cases: Competitive market and a single firm.

If the market is competitive, the firms will produce at a price-quantity pair such that $LRMC =P$. But at this price, the total revenue is negative (since the firm earns 0 profit at $(Q_C,P_C)$).
Thus the firms will be better off shutting down and earning 0 profits. Clearly, a competitive market won't work in such cases.

For a monopoly, the firm will charge price $P_M$ and produce $Q_M$ (the point where $LRMC=MR$). This firm earns a positive profit ($Q_MP_M&gt;LRAC*Q_M$).