(a) Find the consumer's surplus and producer's surplus for the demand function $p_d = 25 - 3x$ and supply function $p_s = 5 + 2x$. OR (b) Compute (i) Laspeyre's (ii) Paasche's (iii) Fisher's Index numbers for the 2010 from the following data. | Commodity | Price 2000 | Price 2010 | Quantity 2000 | Quantity 2010 | | --- | --- | --- | --- | --- | | A | $12$ | $14$ | $18$ | $16$ | | B | $15$ | $16$ | $20$ | $15$ | | C | $14$ | $15$ | $24$ | $20$ | | D | $12$ | $12$ | $29$ | $23$ |

(a) Find the consumer's surplus and producer's sur – Class 12 Business Mathematics Statistics

Question 21 of 42

Find the consumer's surplus and producer's surplus for the demand function $p_d = 25 - 3x$ and supply function $p_s = 5 + 2x$ . OR
Compute (i) Laspeyre's (ii) Paasche's (iii) Fisher's Index numbers for the 2010 from the following data.

Commodity	Price 2000	Price 2010	Quantity 2000	Quantity 2010
A	$12$	$14$	$18$	$16$
B	$15$	$16$	$20$	$15$
C	$14$	$15$	$24$	$20$
D	$12$	$12$	$29$	$23$

Tamil Nadu DgeTamil Nadu HSC (DGE) Commerce Board 2022Subjective· 5mImportance★★★★★

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(a) $p_d=p_s\Rightarrow x_0=4,p_0=13$ ; $CS=24,\ PS=16$ . (b) $L=1280/1200\times100=106.67$ , $P=1040/973\times100=106.89$ , $F=\sqrt{LP}=106.78$ .

(a) Consumer's and producer's surplus.

Equilibrium: $25-3x=5+2x\Rightarrow20=5x\Rightarrow x_0=4,\ p_0=25-3(4)=13.$

Consumer's surplus:

$CS=\int_0^{4}(25-3x)\,dx-p_0x_0=\Big[25x-\tfrac{3x^2}{2}\Big]_0^4-13(4)=(100-24)-52=76-52=24.$

Producer's surplus:

$PS=p_0x_0-\int_0^{4}(5+2x)\,dx=52-\Big[5x+x^2\Big]_0^4=52-(20+16)=52-36=16.$

(b) Index numbers.

Commodity	$p_0$	$p_1$	$q_0$	$q_1$	$p_1q_0$	$p_0q_0$	$p_1q_1$	$p_0q_1$
A	12	14	18	16	252	216	224	192
B	15	16	20	15	320	300	240	225
C	14	15	24	20	360	336	300	280
D	12	12	29	23	348	348	276	276
Total					1280	1200	1040	973
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