Understanding the shape of a Marginal Cost Curve My class IB has just discussed allocative efficiency and hence consumer and producer supply. They explained the concepts with a diagram like this:


It all made perfect sense to me until it was mentioned that the supply curve can also be seen as a marginal cost curve. If this is the case, I don't understand why it is only sloping upwards. I know that marginal cost curves (at least at short-term) look something like... 
But the curve in the first diagram is different.

Is is an oversimplification of a real marginal cost diagram, or am I missing something?
You are missing the average cost curve in the same diagram. 
Basic algebra gives us the following.  

Let's find the minimum of the $AC = C/Q$. We have

$$\frac {\partial AC}{\partial Q} = \frac {MC\cdot Q - C}{Q^2}$$

For this to be equal to zero, we must have $MC \cdot Q = C \implies MC = AC$. So when $AC$ is at its minimum, it equals $MC$. But we also want the second order condition, and we want the second derivative to be positive, evaluated at the critical point.

$$\frac {\partial^2 AC}{\partial Q^2} &lt;0 \implies ...MC'\cdot Q^3-2MC\cdot Q^2 + 2QC &gt;0$$

At the critical point $MC = AC = C/Q$. Inserting this we get the condition 

$$MC'\cdot Q^3-2(C/Q)\cdot Q^2 + 2QC &gt;0 \implies MC'&gt;0$$

So at the point where $MC = AC$ we want MC to be rising. But this implies that it will cross the $AC$ curve from below. In turn this implies that for quantities lower than this point, marginal cost curve will be below the average cost curve, which means that if this left part of $MC$ curve was a supply curve the firm would have losses.  

Therefore the supply curve is only an upwards-sloping part of the marginal cost curve. You can now superimpose the $AC$ curve that is consistent with all these.