Lecture 7: Labor Demand

Transcription

1 Lecture 7: Labor Demand Nicolas Roys University of Wisconsin Madison Econ 302

2 Topics of today s class Last Lecture: I Labor Supply Today s Lecture: I Labor Demand

3 How Much Does the Economy Produce? What determines the quantity of goods and services produced? 2 Key Factors of Production: I N: hoursofworkandnumberofworkers I K: Capital things that last and provide services over a period of time I I Examples: buildings, cars, machines, computers, equipment,... Investment = activity that increases the capital stock Not only Quantity: I z is the level of technology or total factor productivity (TFP) The production function gives output as a function of inputs Y = zk 1 3 N 2 3

4 The Economy of Shangry La I The people of Shangri La love to eat satsumas (a type of mandarin orange). I Production of satsumas: Y = zk 1 3 N 2 3 K = Number of satsuma trees (capital) N = Number of workers Y = Number of satsumas harvested during the year z = Aparameteroftheproductionfunction

5 Example Y = zk 1 3 N 2 3 K = 8trees N = 27 workers z = 2000 Then Y = = 36, 000 satsumas.

6 The Diminishing Marginal Product of Capital Suppose the firm were to vary the stock of capital K (without changing the number of workers N nor technology z)

7 The Marginal Product of Capital 2properties: 1. output is increasing in capital 2. the slope of the production function becomes flatter as capital increases Definition The marginal product of capital is the additional output that can be produced with one additional unit of capital holding labor constant =) It is the slope the production function in the previous figure: output as a function of capital when labor is fixed

8 The Marginal Product of Capital 2propertiesoftheproductionfunctioncanbeexpressedas: 1. MP K > 0 2. MP K is declines as the capital stock is increased: diminishing marginal productivity of capital Example: 1. more satsuma trees =) more output 2. Adding more satsuma trees to Shangri La has a smaller and smaller effect on the total number of satsumas harvested (as there is a limit to how effectively the workers can farm and pick).

9 The Marginal product of labor Definition The marginal product of labor is the additional output that can be produced with one additional unit of labor holding capital constant 1. MP N > 0 2. MP N is declines as the quantity of labor is increased: diminishing marginal productivity of labor Example: 1. more workers =) more output 2. congestion effect : 2.1 When there are few workers in the firm, hiring an additional worker helps increase production a great deal. 2.2 but when there are many workers already, hiring an additional worker is less helpful for production (the firm gets congested)

10 Profit Maximization Problem I Firm rents capital at rate r I Firm hires labor at wage w I wages of the workers they hired is determined in a competitive labor market and not set by the firms themselves I Profits: Output minus Costs I a firm s goal is to earn the highest possible level of profit = zk 1 3 N 2 3 rk wn I Assume that K is fixed: static economy

11 Profit Maximization Problem

12 Profit Maximization Problem Firm chooses N to Maximimize profits : = zf (K, N) rk wn Optimal Choice MP N = w

13 Example F (K, N) = zk 1 3 N 2 3 MP N F (K, = 2 3 zk 1 3 N = z 2 3 Assume. z = K = 1. Labor Demand: 2 3 N 1 3 = w 2 N = 3w 1 K 3 N 3 I w = 2 3, N = 1 I w = 1, N =

14 Labor Demand

15 Development Accounting Look at GDP per capita across countries using the production function: where I K: capital I N: workers I z: TFP Y = zk 1 3 N 2 3

16 Development Accounting per capita GDP y: y = Y N = zk 1 3 N 2 3 N K = z N y = zk where k is capital per person. Output per person is the product of two terms: I z: moreproductiveeconomyarericher I k 1 3 :capitalperperson If we double the amount of capital per person in the economy, we less than double output per person

17 Development Accounting: Same Technology Comparing the model to the data: I measure y as real GDP per person I Measure k as capital per person Two approaches to the productivity parameter: 1. Assume the same across countries z = 1 2. Allow to be different

18 Development Accounting: Same Technology

19 Development Accounting: Same Technology Predicted Per Capita GDP, Production View (U.S.=1) Sharp diminishing returns to capital... Does Burundi have a high MPK or low? What about Japan?

20 Development Accounting: Same Technology I The previous figure suggests a puzzle: poor countries should have a very high marginal product of capital I I but then, firms /entrepneurs would have incentives to move capital out of developing countries yet, this is not the direction observed in the data I I the US has a very large trade deficit since about 30 years The Chinese are saving more than they are investing and much that difference is flowing to the United States I Caselli and Freyer (2007 QJE) use measure of GDP, capital, and the shape of the production function to calculate the marginal product of capital for many countries: I Rich Countries: 8.4% I Poor Countries: 6.9% The actual puzzle is then why the marginal product of capital is not much higher given that poor countries have so little capital?

21 Development Accounting: Same Technology If z = 1ineverycountry: I success: countries are rich or poor according to how much capital per person they have I failures: I I countries are generally much poorer than model suggests countries like Japan and Switzerland, with more capital per worker than the US are not in fact richer

22 Development Accounting: Allowing Technology Differences Recall y = zk 1 3 One way to explain why poor countries are not as rich as their capital would suggest is by having z < 1. I Maybe, for some reason, poor countries are just not very efficient at using their capital and labor (and other inputs).

23 Development Accounting: Allowing Technology Differences I Difficulty: we can measure GDP, capital, and labor, but there is no independent measure of TFP I Solution: we measure TFP as a residual. Weobservedevery quantity in the equation above other than TFP z = y k 1 3 Example Japan. Relative to US values: k = 1.178; y = =) z = = Japan must be sufficiently less productive at using machines, factories, and infrastructure than the US!

24 Development Accounting: Allowing Technology Differences

25 The U.S. and Chinese Production Functions

26 Measuring TFP so the Model Fits Exactly

27 The Importance of Capital versus TFP Which is more important in explaining income differences across countries? I compare the five richest and five poorest economies in 2010: y rich y poor {z } 108 = z rich z poor {z } 18 krich k poor 1 3 {z } 6 TFP is twice as important as capital. I so TFP accounts for 3/4 of cross-country income differences and capital accounts for 1/4 Poor countries are mainly poor because they are so inefficient at using their inputs

28 The Importance of Capital versus TFP This is progress: We ve decomposed the big question What explains cross country differences in per capita GDP? into two separate questions: 1. What explains international differences in capital per person? 2. What explains international differences in productivity?... and we also have a sense as to which is more important for which countries. To answer 1 and 2 we ll need to develop the model further.

29 References and further reading I Williamson, Chapter 4 I Jones, Chapter 4