Question

Part 1. Problems and calculations: 1.(10 total points) You are given the following information for a good. Demand: Qd- 280-70P Supply: Qs=-40 + 30P A) (2 points) What is the equilibrium price of this goodf? B) (2 points) What is the price elasticity of demand at the equilibrium price? C) (2 points) What is the price elasticity of supply at the equilibrium price? D) (2 points) If a $1 per-unit excise tax is levied on the buyers of the good, how much will buyers pay after the tax? E) (2 points) What quantity of the good will be sold after the tax?

Answer 1

A) Equilibrium is when Demand = Supply

Here,

Qd = 280 - 70P

Qs = -40 + 30P

Equilibrium Price = Qd = Qs

280 - 70P = -40 + 30P

280 + 40 = 30P + 70P

320 = 100P

3.2 = P = Equilibrium Price

Equilibrium Quantity = 280 - 70(3.2)

                              = 280 - 224

                              = 56 units

B) Price elasticity of demand = (-1/slope)(P/Qd)

   Rewritting the demand equation in slope intercept form,

Qd = 280 - 70P

(1/70)Qd = 4 - P [Diving whole equation by 70]

   P = 4 - (1/70)Qd

   Therfore slope = (-1/70)

   We know at equilibrium (P,Qd) = (3.2 , 56)

   Price Elasticity of demand = [-1/(-1/70)] [3.2/56]

                                          =70 * 0.05714

                                          = 4

C) Price elasticity of supply = (1/slope)(P/Qs)

    Rewritting the supply equation in slope-intercept form

    Qs = -40 + 30P

    (1/30)Qs = (-4/3) + P

    (1/30)Qs + (4/3) = P

    Therefore slope = (1/30)

    We know at equilibrium (P,Qs) = (3.2,56)

    Price elasticity of supply = [1/(1/30)] [3.2/56]

                                         = 30 * 0.05714

                                         = 1.7142

D) New demand curve = 280 - 70(P-1)

                                 = 280 - 70P + 70

                                 = 350 - 70P

New equilibrium price = 350 - 70P = -40 + 30P

                                    390 = 100P

                                    3.9 = P

The new price is 0.7 more than the previous price so the consumer will pay only 0.7 more i.e 3.9, 0.3 will be paid by the producer