Elasticity of Supply for a Monopolist
Elastic with respect to which variable?
Contrary to what is said in some bachelor textbooks, the monopoly has a supply curve, but it cannot directly be seen on the MR=MC Figure. 
As the price is endogenous in the case of monopoly, the price elasticity of supply is not defined, unless you have some exogenous variable shifting the price. For instance if the inverse output demand function is $p=P(y,z)$ where $z$ denotes an exogenous variable (population size, aggregate unemployment rate, etc), then it is possible to compute the elasticity, even in the case of a monopoly. Then you can compare the responsiveness to shifts to $z$ in both the competitive and the monopoly cases. At the monopoly optimum, the condition $$P(y,z)+\frac{\partial P}{\partial y}(y,z)y=c'(y)$$ implicitly defines the supply function $y^*(z)$ and it can be shown by the implicite function theorem that $$\frac{\partial y^*}{\partial z}(z)=-\frac{\partial P/\partial z +y^*\partial^2P/\partial y\partial z}{2\partial P/\partial y+y^*\partial^2P/\partial y^2-c''},$$ where for simplicity I omitted the arguments of the different functions. From the second order condition for an optimum, we know that the denominator is negative. It turns out that for demand shifts $z$ which increase $P$ the monopoly output increases (provided the term $y^*\partial^2P/\partial y\partial z$ is well behaved, if $P$ is linear in $z$ for instance).  In the competitive case, the comparable expression is $$\frac{\partial y^c}{\partial z}(z)=\frac{\partial P/\partial z }{c''},$$ which is positive as well. Now compare both expressions, and conclude…. As we are interested in elasticities, we should actually compare $$\frac{\partial y^*}{\partial z}\frac{z}{y^*}(z) \text{ and } \frac{\partial y^c}{\partial z}\frac{z}{y^c}(z),$$ and consider that $y^*&gt;y^c$. If the inverse demand is linear, comparison is easy, but is involved in general as it depends on global properties of all functions involved in the expressions above.