Essay frame

A factory's marginal cost is MC = 30 + 0.6x and its fixed cost is Rs. 8,000. (a) Find the total cost function. (b) Find the cost of 100 units. (c) Find the extra cost of raising output from 100 to 200 units. (d) Demand is p = 120 − 2q and the market price is Rs. 40: find the consumer surplus.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Integrate MC. C(x) = ∫(30 + 0.6x) dx = 30x + 0.3x² + K.
2 · Use the fixed cost. C(0) = 8,000, so C(x) = 8,000 + 30x + 0.3x².
3 · Cost of 100 units. C(100) = 8,000 + 3,000 + 3,000 = Rs. 14,000.
4 · Definite integral for the change. ∫ from 100 to 200 of MC dx = 18,000 − 6,000 = Rs. 12,000.
5 · Consumer surplus. At p = 40, q = 40: CS = [120q − q²]₀⁴⁰ − 1,600 = 3,200 − 1,600 = Rs. 1,600.
6 · Draw the surplus. [Demand line from (0, 120) to (60, 0); shade the triangle above p = 40 up to q = 40]
7 · Business link. Consumer surplus is the value buyers get above what they pay; firms use it to judge room for price rises.