Question

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 - D1/2pE PE 300 EPD

Answer 1

We know Under Equilibrium :-

Quantity Demanded = Quantity Supplied

So we can substitute quantity supplied D = 100 and E = 200 in the Demand function

37 DE 100 LE : 200 lo = 450 – D + Yz le : Pe = 300 Et Po Using Pe in lo P = 450 - 0 + L : (300 - E +b) fp = 450 - 0 + 150 - € + lo- bo = 600 - D E ha 600 - D - Po = 1200 – 20 - £) - Transformed lo Using values o D = 100 and E = 200_[Initially 7 Po = 1200 – 2x100) – 200. - 1200 - 200 - 200 Po = 800 Now, PE = 300- E + P . = 300 - 200 + 800

= 100 + 800 le = 900 l So, Initially equilibrium prices lo ase : - l = 800 and Pe = 900 b) After Diamond suffly increases to 200 mile So, 0 = 200 . Using D = 200 in bo transformed to equation - € = 1200 - (2x200) – 200 . = 1200 - 400 -200 .. = 1200 - 600 = 600 - Now, le = 300-200 + 600 Ile = 700) so Now a new fries are :- Po = 600 and P² = 700

So we can see,

Initially when D = 100 and E = 200

• p_{​​​​​​D}​​​​​ = 800 and p_{​​​​​​E} = 900

After when D = 200 and E = 100

• p_{​​​​​​D}​​​​​ = 600 and p_{​​​​​​E} = 700

​​​​​​​​​​​​​​Hence, After the increase in supply of Diamond to 200 units both prices of Diamond and Emerals fell by 200.