Where does stuff come from?

Transcription

1 Where does stuff come from? Factors of production Technology

2 Factors of production: Thanks, Marx! The stuff we use to make other stuff

3 Factors of production: Thanks, Marx! The stuff we use to make other stuff Production function: Y = F (K, L, L)

4 Factors of production: Thanks, Marx! The stuff we use to make other stuff K Capital Production function: Y = F (K, L, L)

5 Factors of production: Thanks, Marx! The stuff we use to make other stuff K L Capital Labor Production function: Y = F (K, L, L)

6 Factors of production: Thanks, Marx! The stuff we use to make other stuff K L L Production function: Y = F (K, L, L) Capital Labor Land

7 Factors of production: Thanks, Marx! The stuff we use to make other stuff K L L Production function: Y = F (K, L, L) Capital Labor Land Thanks, Karl Marx!

8 Returns to Scale How does a change in the inputs affect the output?

9 Returns to Scale How does a change in the inputs affect the output? Constant returns: F (zk, zl) = zf (K, L) = zy

10 Returns to Scale How does a change in the inputs affect the output? Constant returns: F (zk, zl) = zf (K, L) = zy Decreasing returns: F (zk, zl) < zf (K, L) = zy

11 Returns to Scale How does a change in the inputs affect the output? Constant returns: F (zk, zl) = zf (K, L) = zy Decreasing returns: F (zk, zl) < zf (K, L) = zy Increasing returns: F (zk, zl) > zf (K, L) = zy

12 Cobb-Douglas production function: Y = AK α L β

13 Cobb-Douglas production function: Y = AK α L β What determines the returns to scale?

14 Cobb-Douglas production function: Y = AK α L β What determines the returns to scale? A (zk) α (zl) β =

15 Cobb-Douglas production function: Y = AK α L β What determines the returns to scale? A (zk) α (zl) β = z α+β AK α L β

16 Cobb-Douglas production function: Y = AK α L β What determines the returns to scale? A (zk) α (zl) β = CRS: α + β = 1 DRS: α + β < 1 IRS: α + β > 1 z α+β AK α L β

17 Returns to Scale Expect CRS

18 Returns to Scale Expect CRS Give me another Paris

19 Returns to Scale What if we only increase one input? Y = K.3 L.7

20 Returns to Scale What if we only increase one input? Y = K.3 L.7 Y K

21 Returns to Scale What if we only increase one input? Y = K.3 L.7 Y L

22 What does this look like in 3d? Y = K.3 L.7

23 What does this look like in 3d? Y = K.3 L.7 Level curves : L K

24 Why.3 and.7? These are the shares of total income (GDP) we observe going to each group of inputs.

25 Why.3 and.7? These are the shares of total income (GDP) we observe going to each group of inputs. Determined by supply and demand for inputs and their prices: w = labor wage r = capital rental rate

26 Determination of factor prices

27 The Firm s Problem Sell Y at price P Hire L at price w Hire K at price r

28 The Firm s Problem Sell Y at price P Hire L at price w Hire K at price r Goal: maximize profits

29 The Firm s Problem Sell Y at price P Hire L at price w Hire K at price r Goal: maximize profits Profit = Revenue Costs

30 The Firm s Problem Sell Y at price P Hire L at price w Hire K at price r Goal: maximize profits Profit = Revenue Costs = P F (K, L) wl rk Profit maximization rule: MB = MC

31 The Firm s Problem Sell Y at price P Hire L at price w Hire K at price r Goal: maximize profits Profit = Revenue Costs = P F (K, L) wl rk Profit maximization rule: MB = MC MB: extra revenue MC: extra payments to inputs

32 Marginal product What is the marginal benefit of hiring another worker?

33 Marginal product What is the marginal benefit of hiring another worker? MPL = F (K, L + 1) F (K, L) MPL = F L (K, L)

34 Marginal product of labor

35 Marginal product of labor Why does the MPL fall?

36 Marginal Products with Cobb-Douglas MPL = F L (K, L) = βk α L β 1

37 Marginal Products with Cobb-Douglas MPL = F L (K, L) = βk α L β 1 ) α MPL = (1 α) ( K L = (1 α) Y L β = 1 α MPK = α ( ) L 1 α K = α Y K (Remember the power rule!)

38 Profit = Revenue Costs

39 Profit = Revenue Costs Profit = Revenue Costs

40 Profit = Revenue Costs Profit = Revenue Costs Maximum when

41 Profit = Revenue Costs Profit = Revenue Costs Maximum when Profit = 0

42 Profit = Revenue Costs Profit = Revenue Costs Maximum when Profit = 0 Revenue = Costs

43 Profit = Revenue Costs Profit = Revenue Costs Maximum when Profit = 0 Revenue = Costs Profit maximization rule: { P MPL = w MR = MC P MPK = r { MPL = w P MPK = r P

44 Division of National Income Y = L MPL + K MPK + P rofits

45 Division of National Income Y = L MPL + K MPK + P rofits But in a competitive market, profits are zero. This is the same as CRS.

46 Division of National Income Y = L MPL + K MPK + P rofits But in a competitive market, profits are zero. This is the same as CRS. Cobb-Douglas example: L MPL + K MPK ( ) K α ( ) L 1 α = L (1 α) + K (α) L K = (1 α) K α L 1 α + αk α L 1 α = K α L 1 α

47 Income Shares Why.3 and.7? r = MP K = α Y K w = MP L = (1 α) Y L

48 Income Shares Why.3 and.7? r = MP K = α Y K w = MP L = (1 α) Y L Proportion of total income going to capital: rk Y = α

49 Income Shares Why.3 and.7? r = MP K = α Y K w = MP L = (1 α) Y L Proportion of total income going to capital: rk Y = α Proportion of total income going to labor: wl Y = 1 α

50 Income Shares

51 Theory of Everything The magical macro equation: Y = AK.3 L.7