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Imagine there are 2 different types of people who value class size differently. Assume the number of students is fixed thus m

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Answer #1

For understanding this particular question we must know that the MB curve is the demand curve itself and the rising portion of the MC curve is the supply curve as these two integral concepts are applied for solving this problem. Moreover, in this problem MC =60 or P=60 is the supply equation.

There are two categories of consumers who prefer two different types of demand curves as mentioned in type 1 and type 2 MB equations, which are two demand equations for the two categories of consumers.

a.

The two demand equations are:-

P = 100 - Q ... (1)

P = 80 - Q ... (2)

In this particular case, the market demand curve is calculated by adding equation (1) and (2);

\therefore P = 180 - 2Q is the market demand equation.

P = 60 is the supply equation.

Hence, at equilibrium; when demand = supply;

180 - 2Q = 60

\implies2Q = 180 - 60

\therefore Q* = 120 / 2 = 60

This is depicted in the diagram.

Y CONSUMER SURPLUS 180 ( Price) P260 60애 B P2180-28 X 84 CA (oty. از زیر CS Scanned with CamScanner

The Area (\triangleABC) is the consumer surplus.

\therefore Area (\triangleABC) = 1/2 * BC * AB

= 1/2 * 60 * (180-60) = 3600

Hence, the total surplus is 3600 and the equilibrium quantity is 60 teachers.

b.

Now, in this case a democratic step is taken by the social planner of offering a voting right to all the persons from both the categories and the most favoured demand curve shall be taken in practise. After analysing the voting results the type 1 demand curve wins and it is taken into consideration by taking it as a representative demand curve for all the persons and it is imposed on type 2 category persons as well.

It is shown in the diagram below.

Y 1 TYPE 100TA ( Price 1 60 0 P=60 0 C P, 10o-cs > x Х 0 es (ety CS Scanned with CamScanner

Hence, in this case;

Demand curve is P = 100 - Q ... (3)

Supply curve is P =60 ... (4)

At equilibrium; demand = supply;

100 - Q = 60

\therefore Q = 100 - 60 = 40

Area (\triangleABC) is the consumer surplus.

Hence, Area (\triangleABC) = 1/2 * BC * AB

= 1/2 * 40 * (100-60) = 800

Since 800 is the total surplus for type 1 group.

\therefore Total surplus for all the persons present = (800 + 800) = 1600 [\because type 2 has been imposed with the same demand curve]

\therefore Deadweight Loss = Initial Total Surplus - Final Total Surplus = 3600 - 1600 = 2000

c.

In this case a policy of dividing the market into two portions has been practised where the type 1 follows their own demand curve and the type 2 follows their own demand curve. In other words there is absolute freedom in choosing your own demand curve in this case.

Hence, for type 1;

Demand curve is P = 100 - Q ... (5)

Supply curve is P = 60 ...(6)

Hence, at equilibrium, 100 - Q = 60

\therefore Q1 = 100 - 60 = 40

This is depicted in the diagram below.

Y 1 TYPE 100TA ( Price 1 60 0 P=60 0 C P, 10o-cs > x Х 0 es (ety CS Scanned with CamScanner

Consumer surplus is the same as calculated for the type 1 group in part (b) which is equal to 800.

For Type 2;

Demand curve is P = 80 - Q ...(7)

Supply Curve is P = 60 ...(8)

Hence, at equilibrium, 80 - Q = 60

\therefore Q2 = 80 - 60 = 20

This is depicted in the diagram below.

Proiee P260 6o. K P280 ch x X Х Beyaz Loty Area (OJK) - SUPRAVE FOR SURPLUS * TYPE 2 CS Scanned with CamScanner

Consumer Surplus is the area (\triangleJKL).

\therefore Area(\triangleJKL) = 1/2 * JK * KL

= 1/2 * (80-60) * 20

=200

\therefore Total Surplus = Surplus for type 1 + Surplus for type 2 = 800 + 200 = 1000

\therefore Efficient number of teachers to be hired = Q1 + Q2 = (40 + 20) = 60.

d.

The intuition from this following problem says that if all the persons are individually taken care and their demands are inculcated in the market demand curve it yields the highest level of satisfaction in total.

Secondly, if a democratic step is taken where voting rights are offered it yields to a comparatively lesser total satisfaction (surplus).

Lastly, if all the persons are offered freedom to do whatever they want, that leads to anarchism and so the total satisfaction is much lesser than the immediate previous case.

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