Question

For the following set of demand and supply, equations do the following,

1. Find the equilibrium price and equilibrium quantity for each set of equations.
2. Draw each set of equations in a clearly labeled graph and show the equilibrium P and Q.
3. Calculate the producer surplus at the equilibrium P and Q found in b.
4. If the price were to increase, calculate the total new producer surplus. Calculate the gain in the producer surplus
5. If the price were to decrease, calculate the new producer surplus. Calculate the loss in the producer surplus.
6. Draw c, d and e showing all the points/areas.

Show all your workings*

Equation set one

P=50-2Q

P=20+0.5Q

Equation set Two

P=5000-0.5Q

P=250+0.5Q   

Question 2,3,5 and 6 Are crucial.

Thanks

Answer 1

P=50-2Q

P=20+0.5Q

a) Equilibrium occurs when demand equals supply:

50 - 2Q = 20 + 0.5Q

Q = 12

At Q = 12 in demand or supply equation,

P = 26

b)
2 frantity

c) Producer surplus is area of portion B whose sum is (1/2) * (12 - 0) * (26 - 20) = 36

d) If price rises to 28, producer surplus becomes area of portion B + C + D + E + F whose sum is (1/2) * (16 - 0) * (28 - 20) = 64

24t B ico AK -- f Et / Demend 12 16 quantit 1

e) If price falls to 24, producer surplus is area of portion C whose sum is (1/2)* (8 - 0) * (24 - 20) = 16

-Supply 26------ 2 13 is Ruantity

P=5000-0.5Q

P=250+0.5Q

a) Equilibrium occurs when demand equals supply:

5000 - 0.5Q = 250 + 0.5Q

Q = 4,750

At Q = 4,750 in demand or supply equation,

P = 2,625

b)

c) Producer surplus is area of portion B +C whose sum is (1/2) * (4750 - 0) * (2625 - 250) = 5,640,625

d) If price rises to 3500, producer surplus becomes area of portion B + C + D + E + F whose sum is (1/2) * (6500 - 0) * (3500 - 250) = 10,562,500

e) If price falls to 2000, producer surplus is area of portion C whose sum is (1/2)* (3500 - 0) * (2000 - 250) = 3,062,500

frien 5000 .. Supply $ 2625/. 2000 s Dermend 3500 10000 & entity