Is the following graph possible? Is the following graph possible?



I've attempted to sketch the TC/TR curves for it but they don't seem to be able to satisfy the following two properties at the same time:

1) Slope of Total Cost (TC) being less than the slope of Total Revenue (TR) until q=b, that is until quantity is at the zero marginal profit level.

2) TC being lesser than TR at first but going on to be greater than it after q=a, that is after quantity is at the zero economic profit level.
Your basic assumptions seem to be
$$
p(q_a) = AVC(q_a)
$$ 
and as the difference between price and average variable cost is decreasing before $q_a$ and increasing after it you also assume
$$
\frac{d \ \left(p(q) - AVC(q)\right)}{d \ q} &lt; 0.
$$
(More on the necessity of this assumption later.)
 We can rewrite this second assumption to
$$
\frac{d \ p(q)}{d \ q} - \frac{d \ \frac{VC(q)}{q}}{d \ q} = \frac{d \ p(q)}{d \ q} - \frac{MC(q) \cdot q - VC(q)}{q^2} &lt; 0.
$$
Multiplying by $q&gt;0$ yields
$$
\frac{d \ p(q)}{d \ q} \cdot q - MC(q) - AVC(q) &lt; 0.
$$
Adding $p(q) + AVC(q)$ we get
$$
\frac{d \ p(q)}{d \ q} \cdot q + p(q) - MC(q) &lt; p(q) - AVC(q).
$$
The left hand side is now $MR(q) - MC(q)$. It follows from our two initial assumptions that
$$
\forall q &gt; q_a: \ p(q) &lt; AVC(q).
$$ 
Then for such values of $q$
$$
MR(q) - MC(q) &lt; p(q) - AVC(q) &lt; 0.
$$
Because of this there can be no $q_b &gt; q_a$ such that $MR(q_b) = MC(q_b)$.



On the necessity of the second assumption: 
Seems to me that without this assumption the goal function $p(q) \cdot q - C(y)$ would not be concave and hence $MR(q) = MC(q)$ would not be a sufficient condition for optimum.