Log in
HomeClass Notes1,200,000CA670,000

ECON 3411 Lecture Notes - Lecture 27: Sunk Costs, Production Function, Longrun

14 views3 pages
School
York University
Department
Economics
Course
ECON 3411
Professor
Ying Kong

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

Algebraic forms of the production function and productivity. Long-run costs and economies of scale: multiple-output cost functions. F is a functional form relating the inputs to output. The maximum amount of output that can be produced with k units of capital and l units of labor: short-run vs. Period of time where some factors of production (inputs) are fixed, a(cid:374)d co(cid:374)strai(cid:374) a (cid:373)a(cid:374)ager"s decisio(cid:374)s: long-run. Period of time over which all factors of production (inputs) are variable, and can be adjusted by a manager. Productivity measures: total product: total product (tp): maximum output produced with given amounts of inputs, example: cobb-douglas production function: Q = (16). 5 l. 5 = 4 l. 5. Q = 4 (100). 5= 4(10) = 40 units. Productivity measures: average product of an input: average product of an input: measure of output produced per unit of input, average product of labor: apl = q/l. Measures the output of a(cid:374) (cid:862)a(cid:448)erage(cid:863) (cid:449)orker.

Get access

Grade+
$40 USD/m
Billed monthly
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
10 Verified Answers
Class+
$30 USD/m
Billed monthly
Class+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
7 Verified Answers

Related Documents

ECON 3411 Lecture Notes - Lecture 29: Production Function, Marginal Product, Isoquant
magentasardine691
ECON 3411 Lecture Notes - Lecture 28: Production Function, Marginal Product
magentasardine691
ECON 3411
Final Exam
Study Guide
ECON 3411 : Chapter 5 Solution.pdf
erinlocust998

Related Questions

- Essay Question:

Assume a firm uses two inputs in its production process: labour and capital. Using isocost and isoquant analysis, examine the possible effects of an increase in wage on the firm’s

(a) use of labour and capital

(b) long-run total and average costs.

- Problem Question:

a) Derive the cost minimizing input demands and the long-run total cost function for the following production functions assuming input prices w1 and w2:

(i) y = f(x1, x2) = 2x1 + x2

(ii) y = min(x1, 3x2)

b) For each of the production functions above, determine the short-run input demands and short run total cost function when input 2 is limited to x2 = 100 units

3. A firm has a long-run production function:   

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run? 

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

A firm has a production function Q=F(K, L) with the constant return to scale, where k is units of capital and L is united of labour. Input prices are r=$2 per unit of K and w=$1 per unit of L. When it produces 5 units of output, it uses 2 units of capital and 3 units of labour. When its long-run total cost is equal to $70, how much capital and labour it will employ to product how many units of output? What is the long-run average cost?