Is the supply of output for a monopolist less elastic than that of a perfectly competitive firm with the same production function?
On one hand, it seems impossible to calculate the elasticity of supply for a monopolist since it has no supply curve (i.e. no explicit relationship between quantity supplied and prices since it determines both quantity and therefore indirectly, prices by producing where MR = MC). As a result, it would be impossible to calculate the elasticity of supply for a monopolist and the above statement is false.
However, it would seem to make sense that the elasticity of supply is lower for a monopolist because if for example there is an increase in demand, leading to higher prices, the additional output produced by a competitive firm would be higher than a monopolist as the monopolist would tend to restrict output to keep prices higher. Thus, the monopolist's supply is less elastic and responsive to price changes.
Both sets of reasoning seem to be correct to me. What am I missing?