Suppose the market demand curve for a product is given by: Qd = 500 – 15P + 201 and the market supply schedule

Question

Suppose the market demand curve for a product is given by: Qd = 500 – 15P + 201 and the market supply schedule is: Q = -25 + 10P – 10K. The initial values are I = 10, K = 5

a. What are the equilibrium price and quantity in this market?

b. At the market equilibrium, what is the price elasticity of demand and the income elasticity of demand?

c. Suppose K increases to 20, what are the new equilibrium values?

Answer 1

a. sub in I and K at intial values, set Qd=Qs, solve for P, plug back into Qd (or Qs), solve for Q

b. Ed find partial of Qd wrt P mult by P/Q at equil

    Ei  find partial of Qd wrt I  mult by I/Q at value given for I and eqiul value for Qd

c. do a) with new value for K

Answer 2

a)

500-15P+20*10=-25+10P-10*10

825=25P

P=33

Q=205

b)

Point-elasticity method:

(Qd)'=(500– 15P + 20I)' = -15

E(P)=-15*33/205= -2.4146

(Qd)'=(500– 15P + 20I)' =+20

E(I)=20*10/205=0.9756

c)

500-15P+20*10=-25+10P-10*20

925=25P

P=17

Q=445