{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

econ11_08_ps6_sol

# econ11_08_ps6_sol - Eco11 Fall 2008 Simon Board Economics...

This preview shows pages 1–4. Sign up to view the full content.

Eco11, Fall 2008 Simon Board Economics 11: Solutions to Practice Problems 6 (Week 7) November 11, 2008 1. Cost Functions A firms has cost function c ( q ) = 100 - 10 q + 5 q 2 . a) Find the fixed cost. 1 b) Find the variable cost. 2 c) Find the average cost. d) Find the marginal cost. e) Draw the relationship between MC and AC. Prove that they always intersect at the minimum AC. Solution (a) The fixed cost is 100. (b) The variable cost is - 10 q + 5 q 2 . (c) The average cost is AC ( q ) = 100 q - 10 + 5 q (d) The marginal cost is MC ( q ) = - 10 + 10 q (e) AC is a convex function. Differentiating, it is minimised when d dq AC ( q ) = - 100 q - 2 + 5 q = 0 1 Definition: The fixed cost is the cost that is independent of output. 2 Definition: The variable cost is the cost that varies with the level of output. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Eco11, Fall 2008 Simon Board Rearranging, we find that q = 20. We have AC = MC when 100 q - 10 + 5 q = - 10 + 10 q Rearranging, we find that q = 20. 2. Cost Functions A firm has production function f ( z 1 , z 2 ) = z 1 / 2 1 ( z 2 - 1) 1 / 2 The prices of the inputs are r 1 and r 2 . (a) Find MP 1 , MP 2 , and MRTS . (b) If z 2 is fixed at 5, what is the short-run cost function? Find the short-run marginal cost and average cost. (c) What are the long-run input demand functions? What is the long-run cost function? Find the long-run marginal cost and average cost. (d) Does the production function exhibit increasing, constant or decreasing returns to scale. Solution (a) The marginal products are MP 1 = 1 2 z - 1 / 2 1 ( z 2 - 1) 1 / 2 MP 2 = 1 2 z 1 / 2 1 ( z 2 - 1) - 1 / 2 Hence we have MRTS = MP 1 MP 2 = z 2 - 1 z 1 2
Eco11, Fall 2008 Simon Board (b) The cost minimisation problem is to choose z 1 to minimise r 1 z 1 + 5 r 2 subject to 2 z 1 / 2 1 q .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

econ11_08_ps6_sol - Eco11 Fall 2008 Simon Board Economics...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online