# Considering the following Dema

Considering the following Demand curves y1 = 300-3p1 +5p2 and y2 = 400-10p1 + 8p2 corresponding to differentiated butrelated goods and whose choice is simultaneous.

a) Write the equilibrium price equation.b) Calculate the equilibrium price and the quantities sold of good1 and good.

Answer:

From the mathematical standpoint the system is indeterminate -there are four variables to solve for, and only two equations.However with the assumption of a closed system and some economicintuition, we may arrive at a tentative solution.

First, in a closed system with two commodities it is therelative price ratio (p1 / p2) that matters, not the individualprices. We can set the p2 = 1, i.e. assume the second commodity isa numeraire good i.e. an item in terms of which other prices arequoted. This yields

y1 = 305 – 3p || y2 = 408 – 10p

=> (y2 – y1) = 103 – 7p

Thus the **equilibrium price equation** is: [ S2(p)- S1(p) = 103 – 7p ]

Still indeterminate, unless we consider the information aboutdifferentiated but *related* goods. In the absence of betterinformation, we can assume the supply functions of the commodities(which is a really a proxy for firms’ cost functions) to beidentical i.e. their production cost structures are identical.

So at a given price (or price ratio) p, y1 = S1(p) = S2(p) =y2

=> ( y2 – y1) = 0 => [ p = 103/7 ] => **p1 = 103and p2 = 7** (not necessarily as p1/p2 = 103/7 defines aninfinite number of 2-place price vectors but any one is as good asthe other)

**Equilibrium quantities are equal** with y1 = y2 =1826/7