Speaker 0: Hi, everybody, my name's Caroline Elliott, and in this short
Speaker 0: film, I'm going to explain my multivariate calculus is important
Speaker 0: for economists.
Speaker 0: Most specifically, I'll explain.
Speaker 0: My partial differentiation is important for industrial economists like myself.
Speaker 0: As an industrial economist, I look at the strategic decisions
Speaker 0: taken by firms in an oligopoly industry, we assume that
Speaker 0: there are only a small number of firms.
Speaker 0: And crucially, we assume that when those firms make strategic
Speaker 0: decisions, they need to take account of the expected strategic
Speaker 0: decisions of rivals as well.
Speaker 0: So firms decisions are interdependent.
Speaker 0: There are lots of examples of oligopoly industries in the
Speaker 0: real world.
Speaker 0: For example, we can consider the competition between Apple and
Speaker 0: Samsung in the production of mobile phones, or we could
Speaker 0: consider the competition between Coca-Cola and Pepsi.
Speaker 0: We typically assume the oligopoly firms strategically choose levels of,
Speaker 0: for example, outputs or price to maximise profits.
Speaker 0: We can extend the analysis and assume that a firm
Speaker 0: chooses the level of output and advertising and maybe research
Speaker 0: and development all simultaneously to maximise its profits.
Speaker 0: But in this film, to keep the analysis simple, we're
Speaker 0: going to assume that our oligopoly firms are just choosing
Speaker 0: levels of output to maximise profits.
Speaker 0: We can think about an individual firm wanting to choose
Speaker 0: output level QSI to maximise its profits pie, and we
Speaker 0: can plot this firm's profit function as a function of
Speaker 0: its output.
Speaker 0: And we see that initially, as output increases, profits will
Speaker 0: rise.
Speaker 0: However, if output continues to rise, eventually profits will start
Speaker 0: to fall.
Speaker 0: So the challenge facing Funmi is to select the level
Speaker 0: of output QSI associated with profits being maximised.
Speaker 0: And we see that profits will be maximised where the
Speaker 0: slope of the profit function is equal to zero.
Speaker 0: Now, that may make us think that to identify the
Speaker 0: profit maximising level of output QSI, we should take the
Speaker 0: derivative of the profit function pie with respect spectacular AQI,
Speaker 0: and that will give us the slope of the profit
Speaker 0: function and set that equal to zero.
Speaker 0: However.
Speaker 0: The problem is that the profits of I don't just
Speaker 0: depend on the outputs of I, but also on the
Speaker 0: outputs of any other firms.
Speaker 0: So we shouldn't just take an ordinary derivative, which would
Speaker 0: give us a slope of a profit function and set
Speaker 0: it equal to zero to identify the outputs associated with
Speaker 0: profits being maximised.
Speaker 0: But instead, if we want to take account of the
Speaker 0: fact that profits depend on the output of AI and
Speaker 0: sun, then we need to take a partial derivative of
Speaker 0: the profit function and set that equal to zero and
Speaker 0: then the remaining fields in the section you will learn
Speaker 0: how to calculate such partial derivatives.
Speaker 0: OK, thank you.