Question

Partial Competitive Equilibrium Suppose households consider diamonds (D) and emeralds (E) as substitutes. Let the supply of both be fixed in the market period at D 100 and E 200. The inverse demand functions for diamonds and emeralds are give by: 3. Po 450 - D + 1/2pE PE= 300 - E pD What are the equilibrium prices of diamonds and emeralds? а.

Answer 1

Use D = 100 and E = 200 in demand functions

Pd = 450 - 100 + 0.5Pe or Pd - 0.5Pe = 350

Pe = 300 - 200 + Pd or Pe - Pd = 100

Now we have Pd - 0.5Pe = 350 and Pe - Pd = 100

This becomes

Pe - (350 + 0.5Pe) = 100

0.5Pe = 450

Pe = 900 and so Pd = 800

Hence equilibrium prices are Pe = 900 and Pd = 800