Page 141 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists

Note Therefore, 20 = 140 – 6q
Or 6q 140 20 120

q = 20 or p = 20
And p = – 60
Profit would be positive.
Example 13: Following is the demand and cost function of two separate markets
−
−
+8.

In case of price difference, determine the price, production, marginal revenue and total profit of
production of both the two markets.
Solution: We know that
P = 80 – 5q 1 ...(i)
1
P = 180 – 29q 2 ...(ii)
2
C = 50 + 20 (q + q ) ...(iii)
1
2
Total revenue of first market
R =P q = (80 – 5q ) q 1
1
1
1 1
=80q – 5q 2 1 ...(iv)
1
Total revenue of second market
R = p q = (180 – 29q ) q 2
2 2
2
2
= 180q – 29q 2 2 ...(v)
2
By partially differentiating equation (iv) with respect to q , equaling it to Zero
1
w R 1

MR = q w 1 80 10q 2 0 ...(vi)
1
Or 10q = 80 or q = 8
1
1
Similarly by partially differentiating equation (v), equaling it to Zero
w R 2

MR = q w 2 180 58q 1 0 ...(vii)
2
180 90
Or 58q = 180 or q 2 58 29
2
Total Profit p = R + R – C
2
1
2
= 80q 5q 180q 2 29q 2 2 50 20q 1 20q 2
1
1
2
= 60q 5q 160q 2 29q 2 2 50 ...(viii)
1
1
Putting the value of q and q in equations (i), (ii), (vi), (vii) and (viii)
1 2

P = 80 5 8 u 80 40 40
1
90

P = 180 29 u 29 180 90 90
2
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