Question

2. (15) Social Surplus Analysis The table below describes a market with two consumers and two producers. It gives each consumer's demand curve and each producer's supply curve for integer quantities of the good. The demand and supply curves are all linear. Let p denote price, and q quantity Price S5 Firm 1SFirm2S_Agg S 10 Cons 1 D Cons 2 D Agg D 12.5 10 7.5 4 S3 S2 S1 4 4 4 2.5 10 a) (3) Fill in the numbers in the two blank columns. What are the equilibrium quantity and the equilibrium price? Draw a diagram displaying the aggregate demand (Agg D) and aggregate supply (Agg S) curves b) (3) State the two assumptions under which the aggregate marginal social benefit curve coincides with the aggregate demand curve, and the single assumption under which the aggregate marginal social cost curve coincides with the aggregate supply curve c) (3) On the assumptions that the aggregate marginal social benefit curve coincides with the aggregate demand curve and that the aggregate marginal social cost curve coincides with the aggregate supply curve, calculate the (dollar) social benefit at the equilibrium, the (dollar) social cost at the equilibrium, and the (dollar) social surplus at the equilibrium. (Recall that the area of a triangle is one-half the base times the height). d) (3) Write down the algebraic equations for the aggregate demand and aggregate supply curves, and verify that their point of intersection gives the same equilibrium quantity and price that you obtained in a) e) (3) Decompose the social surplus you have calculated in c) into consumer surplus, producer surplus, and government surplus

Answer 1

a)

Price	Cons 1 D	Cons 2 D	Agg D	Firm 1 S	Firm 2 S	Agg S
5	0	0	0+0=0	10	12.5	10+12.5=22.5
4	1	2	1+2=3	8	10	8+10=18
3	2	4	2+4=6	6	7.5	6+7.5=13.5
2	3	6	3+6=9	4	5	4+5=9
1	4	8	4+8=12	2	2.5	2+2.5=4.5
0	5	10	5+10=15	0	0	0+0=0

b) The aggregate demand curve can be coincide with social benefit curve under following assumptions

i)The aggregate demand curve can coincide with social benefit curve only when the consumption of one consumer does not allow to generate negative externalities. It means consumer 1 demanded and consumed or consumer 2 demanded and consumed and from there no negative externalities will arise.

ii) The demand and consumption of one consumer will not generate any positive externalities to another customer. It means from from demand and consumption there will not arise any positive externalities to another consumer.

The aggregate supply curve can coincide with marginal social cost curve under following assumption-

I) From production there will not arise any positive or negative externalities so the supply curve will be itself marginal social cost curve.

C) The equilibrium will take place when aggregate demand and aggregate supply becomes both 9. Equilibrium price will be $2. At this price of $2 and equilibrium quantity of 9 units the aggregate social benefit at equilibrium will be 1/2*9*3= 13.5 + 9*2=31.5. Aggregate social cost will be 1/2*2*9=9. Social surplus = 31.5 - 9=22.5.

D) Aggregate demand equation can be written as Qd = 15-3p, aggregate supply equation can be written as Qs= 4.5p. By equating demand supply we get p=2, qd and qs=9.