1. A firm in a perfectly competitive market has the following cost function:

C = 1/3q³ - 5q² + 30q +10

If the market-clearing price is 6, obtain the profit maximising level of output.

2. Discuss the importance of the Hawkins-Simon conditions in input-output analysis.

B. Medium Answer

3. Find the short run average cost for the production function q = AL^1/3K^2/3 where total cost (TC) = wL + rK, the symbols having their usual meaning.

4. i) Let Y = 2x² + 3x +1 / 3x² - 4x + 1

For what values of x will be the function be discontinuous?

ii) Show that

a₁x₂ + b₁x + c₁ /a₂x₂ + b₂x + c₂

tends to a₁/a₂ as x → ∞

5. Determine the distance between the points:

i) (3,0,7) and (-4,8,2)

ii) (4,6,7,1) and (-3,0,2,4)

iii) The distance between the points (3,1,2,4) and (4,6,5, λ) is 200. What can be said about the value of λ?

C.

6. Define

a. Adjugate of a matrix

b. Decomposable matrix

c. Singular matrix

7. If the demand function for a good is Q = 140 - 5P, what is the price elasticity of demand at P = 15 rupees?

8. Integrate:

(i) x Sinx

(ii) √(a² - x²)dx