TOOLS OF ANALYSIS FOR INTERNATIONAL TRADE MODELS
Topic 2.3
Let’s try applying a little calculus
Π = Pt T + Ps S
where Π = profit
Pt, Ps = prices of T, S
T, S = outputs of T, S
this is an endowment model so costs are zero, the firm is simply trying to maximize revenue
dΠ = Pt ∆T + Ps ∆S
at the profit maximization point dΠ = O
so Pt ∆T + Ps ∆S = O
so Ps/Pt = - ∆T/ ∆S (1)
(by the way firms act competitively and so they treat prices as parameters, not variables)
(1) says that production will be chosen so that the point on the PPF will have the same slope as the ratio of prices.
another way of describing this:
· Ps/Pt is outside the control of the firm because it is determined by consumers
· the firm wants (1) to be true
· the firm will increase T and decrease S or the opposite (moving along the PPF) until (1) is true
· once (1) is true the firm will stop and remain at that point on the PPF forever until there is a change in Ps/Pt
· the firm is reacting to price changes, not attempting to influence them
what if we are at a point like ‘U’ on the PPF where
-Ps/Pt < ∆T/ ∆S (assuming CIC0 determines prices via tangency)
(when we are looking at negative slopes the steeper slope has a lower numerical value)
to rephrase, the CIC curve has a steeper slope than the PPF at U
so 0 < ∆T/∆S + Ps/Pt (2)
given that we are at U, let us consider what would happen if we increased S production
so ∆ S > 0
Multiply both sides of (2) by Pt ∆S
then Ps ∆S + Pt ∆T > 0
so we will increase Π if we increase S
If we were starting on the PPF to the right of X (at a point like Y) similar reasoning would show that we could increase Π by decreasing S production.
Intuitively, the ‘U’ point is a situation where the price of S is relatively high compared to the price of T and the opportunity cost of increasing S production (T sacrificed) is low. So the firm figures that it will make more profit by ↑ S and selling it at the ‘high’ price of S, even after factoring in the loss of revenue from decreasing production of T.
At this point it’s worth pointing out that the model does not really have a mechanism for determining what prices will actually be at ‘U’ We are just assuming that somehow the prevailing market price will be close to the slope of CIC0 at ‘U’ because of ‘consumer demand’
