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ECON101 Lecture Notes - Lecture 20: Production Function, Marginal Product, Market Power

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School
University of Waterloo
Department
Economics
Course
ECON101
Professor
Nafeez Fatima

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ECON101 Lecture 19: lecture 19

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ECON101 Lecture Notes - Lecture 20: Production Function, Marginal Product, Market Power

21

ECON101 Lecture Notes - Lecture 21: Profit Maximization

Document Summary

Lecture 20: difference between short run and long run: In the short run, at least one of the inputs is fixed. In the long run, all inputs are variable. In the short run, the plant size is fixed but labour can be changed. i. e. capital is fixed but labour can be changed. In the long run, the plant size is variable. Y f (k,l) i. e. output is a function of capital and labour no bar on f b/c not fixed anymore. 27: marginal product of labour: change in total product due to change in labour (change in. If output changes by the same proportion, then the production function exhibits constant returns of scale / no economies of scale in production. If output changes by more than proportion, then the production function exhibits increasing returns of scale / economies of scale.

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Related Questions

Ā Consider a firm whose technology is given by the production function: y = f (K,L) = (N+1)L + 2āˆšK. Assume that input prices for labour, L, and capital, K, are w = 1 and r = 2 respectively. a)Find the firmā€™s short run total cost function assuming the firm cannot hire more workers nor fire its only worker, i.e. L = 1 is fixed.Ā 

b)Find the firmā€™s short run marginal cost, average variable cost and average fixed cost. Draw the three of them in the same graph. What is the short-run supply of the firm?

c)Find the firmā€™s long run total cost function, i.e. when all factors are variable.Ā 

d)Find the firmā€™s long run marginal cost and average cost. Draw them in the same graph. What is the long-run supply of the firm?

- 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 firmĆ¢Ā€Ā™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

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?