Beg to differ on 25th. Firm A can operate in a competitive market with p=1.
However firm B, on increasing output increases its revenue, so it makes positive profits hence can't work as a competitive market entity. It can flood the market at the "competitive price" or offer a little lower price than the marginal cost of "competitive" producers hence capture the whole market.
Firm A can operate only when p>1. It'll shut if p<=1.
Firm B can operate at any p. B doesn't have to produce large output. It can just produce 1 unit and stop there.
More output for B== More profits for B. If you plot MR and MC for B, you'll find that their difference gets large as output increases. So why would it not produce more output? If someone initially operating as a competitive firm gets his hands on such a technology would he not decrease price charged and capture the whole market?
And are we in agreement that A "can" be a competitive firm at some price (p=1?)
That makes sense, but can you quote a source?
Picked up from google:
"While the long run aggregate supply curve is vertical, the short run aggregate supply curve is upward sloping. There are four major models that explain why the short-term aggregate supply curve slopes upward. The first is the sticky-wage model. ... The fourth is the sticky- price model"
In sticky price model that google mentions we assume that a fraction 'f' of firms keep prices constant while remaining fraction (1-f) change it. I don't think question meant that.
22. As function is non homogenous, we shouldn't use this short cut method, instead find the cost function.. (Varian has defined return of scale in average cost term.)
Not the solution but I thought of the problem as a utility function with x and y as perfect complements, as for every optimal x, optimal y also increases. Since these are well behaved preferences, they'll be convex.