Marginal Rate of Technical Substitution

1. Consumer’s problem • Which factors determine consumer’s choice?

2. Single consumer’s demand function

3. What happens when some variables change? • Income changes • Price changes • Why is this important?

4. Example of an economic model: • Difference between exogenous and endogenous variables. • Role of the assumptions New topic: Producer’s Choice

Key question:

Price What factors influence supply?

Supply

700 Eu •

400 Eu •

0 600 1500 Quantity Firm’s decisions

Each firm has to decide

1. To operate or not?

2. Which product(s) to produce?

3. Which materials and in which combinations to use?

4. How many units to produce? Production Function

Resources, such as labor and capital equipment, that firms use to manufacture goods and services are called inputs or factors of production. The amount of goods and services produced by the firm is the firm’s output.

The production function gives the maximum amount of output the firm can produce for any given quantity of inputs. Production Function

The production function gives the maximum amount of output the firm can produce for any given quantity of inputs.

Example: One input 1 Q  f (L)  L2

Q = f(L)

D 7 •

4 • C

Labor 16 49 Example

Suppose that a firm produces only with labor and the production function is 푄 = 퐹 퐿 = 퐿

That is, L units of labor produce 퐿 units of output.

If the firm has to pay a wage of w=$10 for each unit of labor and can sell each unit of output for the price p=$10, how many units will the firm produce? Production Function

Ipad 2: • The tablet itself is assembled in China (and by the end of 2011 also in Brazil) by Taiwan-based Foxconn. • The displays are believed to be manufactured by LG Display and, more recently, by Samsung, both of which are based in South Korea. • The distinctive touch panel is produced by Wintek, a Taiwan-based company that also owns plants in China, India, and Vietnam. • The case is provided by another Taiwanese company, Catcher Technologies, with operations in Taiwan and China. • The battery pack, also originates in Taiwan and is sold by Simplo Technologies and Dynapack International. • A variety of chips and other small technical components provided by various firms, non-exhaustive list includes Korea’s Samsung (again), which is believed to manufacture the main processor (designed by Apple) and possibly the flash memory, Japan’s Elpida contributing the SDRAM, Germany’s Infineon and US Qualcomm both supplying 3G modules, and Italo-French STMicroelectronics, Japan’s AKM Superconductors, and US TAOS each contributing key sensors. Production Function

The marginal product of an input is the change in output that results from a small

change in the input : MPL =  F(L)/L

The average product of an input is the total output divided by the quantity of the

input: APL=F(L)/L

Increasing returns to labor: the production function increases with labor: “the more workers, the more output”.

We say that there are increasing marginal returns to labor if the marginal productivity of labor is increasing (that is, the slope of the production function increases)

We say that there are diminishing marginal returns to labor if the marginal productivity is decreasing. Production Function

Q  f (L)

Q Increasing returns

Increasing Decreasing Decreasing marginal returns marginal returns returns

Labor Production Function: Two Inputs

Two inputs: Labor and Capital 1 1 Example: Q  f (L, K)  L2 K 2

The marginal product of an input is the change in output that results from a small change in an input holding the levels of all other inputs constant.

Change in the quantity of output, Q MP  L Change in the quantity of Labor, L K isheldconst

F(L, K) MP (L, K)  L L K is held const

F(L, K) MP (L, K)  K K L is held const Example

1 1 Q  f (L, K)  L2 K 2

K: 0 10 20 30 40 50 L: 0 0 0 0 0 0 0

10 0 10 14 17 20 22

20 0 14 20 24 28 32

30 0 17 24 30 35 39

40 0 20 28 35 40 45

50 0 22 32 39 45 50

Isoquant

12 An isoquant traces all the combinations of inputs (labor and capital) that produce the same amount of output.

K All combinations of (L,K) along the isoquant produce Q units of output.

Does the figure remind you of anything from consumer theory?

Q = 32 Q = 14 L Example

K 1 1 Q  f (L, K)  L2 K 2

K: 0 10 20 30 40 50 20 • • L: 0 0 0 0 0 0 0

10 0 10 14 17 20 22

20 0 14 20 24 28 32

30 0 17 24 30 35 39 Q = 32 40 0 20 28 35 40 45 Slope=-K/L Q = 14 50 0 22 32 39 45 50

10 50 L Marginal rate of technical substitution

14 The marginal rate of technical substitution between labor and capital, 푀푅푇푆 (퐿 , 퐾 ), is the negative of the slope of the isoquant that goes through 퐿, 퐾 0 0 퐿0, 퐾0. It measures the rate at which the firm can exchange labor for capital and still produce the same output as before.

The marginal rate of technical substitution is (minus) the slope of the isoquant curve:

MRTSL,K = -K/L (for a constant level of output)

Marginal products and the MRTS are related: F(L, K) K MP (L, K) MRTS (L, K)    L  L L,K F(L, K) L MPK (L, K) K Marginal rate of technical substitution

Properties of MRTS:

1. If both marginal products are positive, the slope of the isoquant is negative.

2. If the MRTS also diminishes as the quantity of labor increases along an isoquant, the isoquants are convex to the origin. Returns to scale

How much will output increase when all inputs increase by a particular factor?

We say that a production function f (K, L) exhibits: 1. Increasing returns to scale if f (K,L)  f (L,K) for  1 2. Decreasing returns to scale if f (K,L)  f (L,K) for  1 3. Constant returns to scale if f (K,L)  f (L,K) for  1 Returns to scale: examples

1. A hair salon can produce 100 haircuts a day if it employs 10 hairdressers and 160 haircuts a day if it employs 20 hairdressers. Is the salon’s production function exhibiting decreasing, increasing, or constant returns to scale?

2. A café needs exactly one baker and 30kg of ingredients to produce 30 cakes a day. What is the café’s cake production function? Does it have decreasing, constant, or increasing returns to scale?

3. A firm’s production function is F(K,L) = KaLb. For which values of a and b are its returns to scale increasing? Decreasing? Constant?