PLEASE SHOW ALL WORK Suppose that Q_d = kP and Q_s = c(P - T_o) Are the demand a

Question

PLEASE SHOW ALL WORK

Suppose that Q_d = kP and Q_s = c(P - T_o) Are the demand and supply curves for a commodity whose price is P. T_o is sales tax imposed by the government on sales of this commodity. Compute the price elasticity of demand and the price elasticity of supply of this commodity. The elasticity formula is given as e = dQ/dP P/Q, where e denotes the price elasticity. Be sure to make all the necessary substitutions and solve for each case. Find an expression for P/T_o, where P is the equilibrium price in this market. Under which conditions the following is satisfied: 0

Explanation / Answer

Qd = kP

Qs = c x (P - T0)

(a)

Price elasticity of demand = (dQd / dP) x (P / Qd)

= k x (P / kP) = k x (1 / k)

= 1

Price elasticity of supply = (dQs / dP) x (P / Qs)

= c x [P / {c x (P - T0)}] = (c x P) / [c x (P - T0)]

(b)

In equilibrium, Qd = Qs

k x P = c x (P - T0)

k x P = c x P - c x T0

c x T0 = P x (c - k)

P = c x T0 / (c - k)

So,

dP / dT0 = c / (c - k)

0 < dP / dT0 < 1 means

0 < [c / (c - k)] < 1

0 < c < c - k

c - k > c

- k > 0 (Assuming c is not equal to 0)

k < 0 and c is not equal to zero (Required conditions)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.