Consider the newly established firm Superb PPE Equipment characterised by a production technology, which can be formalised as a Cobb-Douglas function.

Now, describe the key features (e.g. marginal functions, elasticities, etc.) of such a production function. Assume the Superb PPE Equipment needs to decide the optimal combination of capital and labour for its production. How could the Superb PPE Equipment set up a constrained optimisation problem? Provide a step-by-step description of the relevant passages to solve the Superb PPE Equipment constrained optimisation problem in such a first scenario?

Now consider a second scenario in which the only change relatively to the first scenario is that Superb PPE Equipment faces an increase in the overall cost of capital equal to 10% of the first-scenario price due to the new financial market conditions. How would this price increase affect (if at all) the optimal combination of inputs? Discuss the equilibrium in the second scenario (also in comparison to the first one). Would there be any change across scenarios respectively in the quantity produced, the total cost and overall profits?

Please, clearly state any relevant assumption made and write your answer in your own word, while providing the relevant economic intuitions/interpretations beyond the mathematical ones.