Question

Take Home 3 Math 1520 1. Consumer and Producer Surplus. Round answers to the nearest whole number. a) Find the consumer and producer surpluses at the equilibrium (X.P). P. (*) - 6/78 - Demand price p.(x) = 3 102+x Supply price b) Find the new equilibrium and surpluses for the outward shift in demand P. (x)=683-X Demand price Ps(x) = 3/102 + x Supply price

consumer and producer surplus

Answer 1

Pd = 6 rt(78 - x)

Pd² = 36 (78 - x) = 2808 - 36x............(1)

Ps = 3 rt(102 + x)

Ps² = 9 (102 + x) = 918 + 9x...................(2)

At equilibrium (1) = (2)

2808 - 36x = 918 + 9x

x = 42

Put X in (1) or (2), P = 36

Thus this makes equilibrium price as 36 and equilibrium quantity as 42.

Initial consumer surplus is the area of triangle ABC which is 1/2 * (53 - 36) * 42 = 357

Initial consumer surplus is the area of triangle BCD which is 1/2 * (36 - 30.3) * 42 = 119.7

When demand changes to Pd = 6 rt(83 - x)

Pd² = 36 (83 - x) = 2988 - 36x..........(3)

New equilibrium is (2) = (3)

918 + 9x = 2988 - 36x

x = 46

Put value of x in (2) or (3), P = 36.5

Thus this makes new equilibrium price as 36.5 and equilibrium quantity as 46.

New consumer surplus is the area of triangle EDF which is 1/2 * (54.6 - 36.5) * 46 = 417.68

New consumer surplus is the area of triangle EDA which is 1/2 * (36.5 - 30.3) * 46 = 142.6

0 0 Price (P) & A 2.66 AS 36-5 -- 36 te 30.2014 1 Mb 42