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Section 3 – Theory of the Firm

Section 3 – Theory of the Firm. Thus far we have focused on the individual consumer’s decisions: Choosing consumption and leisure to: Maximize Utility Minimize Income Section 3 deals with another economic agent, the producer, and their decisions: Choose inputs, production in order to:

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Section 3 – Theory of the Firm

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  1. Section 3 – Theory of the Firm • Thus far we have focused on the individual consumer’s decisions: • Choosing consumption and leisure to: • Maximize Utility • Minimize Income • Section 3 deals with another economic agent, the producer, and their decisions: • Choose inputs, production in order to: • Minimize Costs (to hopefully maximize profits)

  2. Section 3 – Theory of the Firm In this section we will cover: Chapter 6: Inputs and Production Functions Chapter 7: Costs and Cost Minimization Chapter 8: Cost Curves

  3. Chapter 6: Inputs and Production Functions Consumer Theory Theory of the Firm Goods Utility Inputs Production Profits

  4. Chapter 6: Inputs and Production Functions In this chapter we will cover: 6.1 Inputs and Production 6.2 Marginal Product (similar to marginal utility) 6.3 Average Product 6.4 Isoquants (similar to indifference curves) 6.5 Marginal rate of technical substitution (MRTS, similar to MRS) 6.6 Special production functions (similar to special utility functions) 6.7 Technological Progress

  5. 6.1 Inputs and Production Inputs: Productive resources, such as labor and capital, that firms use to manufacture goods and services (also called factors of production) Output: The amount of goods and services produced by the firm Production:transforms inputs into outputs Technology: determines the quantity of output possible for a given set of inputs.

  6. More Terms Production function: tells us the maximumpossible output that can be attained by the firm for any given quantity of inputs. • Q = f(L,K,M) • Q = f(P,F,L,A) • Computer Chips = f1(L,K,M) • Econ Mark = f2(Intellect, Study, Bribe)

  7. Production and Utility Functions • In Consumer Theory, consumption of GOODS lead to UTILITY: U=f(kraft dinner, wieners) • In Production Theory, use of INPUTS causes PRODUCTION: Q=f(Labour, Capital, Technology)

  8. Production Function Notes • A technically efficientfirm is attaining the maximum possible output from its inputs (using whatever technology is appropriate) • A technically inefficientfirm is attaining less than the maximum possible output from its inputs (using whatever technology is appropriate)

  9. Notes on the Production Function • production set : all points on or below the production function • Note: Capital refers to physical capital • (goods that are themselves produced goods) and not financial capital (the money required to start or maintain production).

  10. Q Example: The Production Function and Technical Efficiency Production Function Q = f(L) D • C Inefficient point • • B Production Set L

  11. Causes of technical inefficiency: • Shirking • -Workers don’t work as hard as they can • -Can be due to laziness or a union strategy • 2) Strategic reasons for technical inefficiency • -Poor production may get government grants • -Low profits may prevent competition • 3) Imperfect information on “best practices” • -inferior technology

  12. Example: Acme medical equipment faces the production function: Q=K1/2L1/2 Given labour of 10 and capital of 20, is Acme producing efficiently by producing 12 units? What level of production is technically efficient?

  13. Example: Q =K1/2L1/2 =201/2101/2=14.14 Acme is not operating efficiently by producing 12 units. Given labour of 10 and capital of 20, Acme should be producing 14.14 units in order to be technically efficient.

  14. 6.2 Marginal Product • The production function calculates TOTAL PRODUCT • Marginal Product of an input: the change in output that results from a small change in an input holding the levels of all other inputs constant. MPL = Q/L (holding constant all other inputs) MPK = Q/K (holding constant all other inputs)

  15. Marginal Utility and Marginal Product • In Consumer Theory, marginal utility was the slope of the total utility curve • In Production Theory, marginal product is the slope of the total product curve:

  16. Q L MPL increasing MPL becomes negative MPL MPL decreasing L

  17. Law of Diminishing Returns • Law of diminishing marginal utility:marginal utility (eventually) declines as the quantity consumed of a single good increases. • Law of diminishing marginal returnsstates that marginal products (eventually) decline as the quantity used of a single input increases. • Generally the first few inputs are highly productive, but additional units are less productive (ie: computer programmers working in a small room)

  18. Q Example: Production as workers increase Each Additional worker Is less productive Each Additional worker Decreases Production Each Additional worker Is equally productive Each Additional worker Is more productive Total Product L

  19. 6.3 Average Product Average product:total output that is to be produced divided by the quantity of the input that is used in its production: APL = Q/L APK = Q/K Example: Q=K1/2L1/2 APL = [K1/2L1/2]/L = (K/L)1/2 APK = [K1/2L1/2]/K = (L/K)1/2

  20. Marginal, and Average Product • When Marginal Product is greater than average product, average product is increasing -ie: When you get an assignment mark higher than your average, your average increases • When Marginal Product is less than average product, average product is decreasing -ie: When you get an assignment mark lower than your average, your average decreases Therefore Average Product is maximized when it equals marginal product

  21. Q L APL increasing APL decreasing APL MPL APL maximized APL L MPL

  22. 6.4 Isoquants Isoquant: traces out all the combinations of inputs (labor and capital) that allow that firm to produce the same quantity of output. Example: Q = 4K1/2L1/2 What is the equation of the isoquant for Q = 40? 40 = 4K1/2L1/2 => 100 = KL => K = 100/L

  23. …and the isoquant for Q = Q*? Q* = 4K1/2L1/2 Q*2 = 16KL K = Q*2/16L

  24. K Example: Isoquants All combinations of (L,K) along the isoquant produce 40 units of output. Q = 40 Q = 20 Slope=K/L L 0

  25. Indifference and Isoquant Curves • In Consumer Theory, the indifference curve showed combinations of goods giving the same utility • The slope of the indifference curve was the marginal rate of substitution • In Production Theory, the isoquant curve shows combinations of inputs giving the same product • The slope of the isoquant curve is the marginal rate of technical substitution:

  26. 6.5 Marginal Rate of Technical Substitution (MRS) Marginal rate of technical substitution (labor for capital):measures the amount of K the firm the firm could give up in exchange for an additional L, in order to just be able to produce the same output as before. Marginal products and the MRTS are related: MPL/MPK = -K/L = MRTSL,K

  27. Marginal Rate of Technical Substitution (MRS)

  28. The marginal rate of technical substitution, MRTSL,K tells us: • The amount capital can be decreased for every increase in labour, holding output constant OR • The amount capital must be increased for every decrease in labour, holding output constant -as we move down the isoquant, the slope decreases, decreasing the MRTSL,K -this is diminishing marginal rate of technical substitution -as you focus more on one input, the other input becomes more productive

  29. MRTS Example Let Q=4LK MPL=4K MPK=4L Find MRTSL,K MRTSL,K = MPL/MPK MRTSL,K =4K/4L MRTSL,K =K/L

  30. Isoquants – Regions of Production • Due to the law of diminishing marginal returns, increasing one input will eventually decrease total output (ie: 50 workers in a small room) • When this occurs, in order to maintain a level of output (stay on the same isoquant), the other input will have to increase • This type of production is not economical, and results in backward-bending and upward sloping sections of the isoquant:

  31. K Example: The Economic and the Uneconomic Regions of Production Isoquants MPK < 0 Uneconomic region Q = 20 MPL < 0 Economic region Q = 10 L 0

  32. Isoquants and Substitution • Different industries have different production functions resulting in different substitution possibilities: • ie: In mowing lawns, hard to substitute away from lawn mowers • In general, it is easier to substitute away from an input when it is abundant • This is shown on the isoquant curve

  33. MRTSL,K is high; labour is scarce so a little more labour frees up a lot of capital K MRTSL,K is low; labour is abundant so a little more labour barely affects the need for capital • • L

  34. MRTS Example Let Q=4LK MPL=4K MPK=4L MRTSL,K =K/L Show diminishing MRTS when Q=16. When Q=16, (L,K)=(1,4), (2,2), (4,1) MRTS(1,4)=4/1=4 MRTS(2,2)=2/2=1 MRTS(4,1)=1/4

  35. K MRTSL,K =4 • 4 MRTSL,K =1 MRTSL,K =1/4 • 2 • 1 Q=16 L 1 2 4

  36. When input substitution is easy, isoquants are nearly straight lines K When input substitution is hard when inputs are scarce, isoquants are more L-shaped 170 130 100 L 55 100

  37. Returns To Scale • How much will output increase when ALL inputs increase by a particular amount? • RTS = [%Q]/[%(all inputs)] 1% increase in inputs => more than 1% increase in output, increasing returns to scale. 1% increase in inputs => 1% increase in output constant returns to scale. 1% increase in inputs => a less than 1% increase in output, decreasing returns to scale.

  38. Example 1: Q1 = 500L1+400K1 Q1 * = 500(L1)+400(K1) Q1*= 500L1+400K1 Q1*= (500L1+400K1) Q1*= Q1 So this production function exhibits CONSTANT returns to scale. Ie: if inputs double (=2), outputs double.

  39. Example 2: Q1 = AL1K1 Q2 = A(L1)(K1) = + AL1K1 = +Q1 so returns to scale will depend on the value of +. + = 1 … CRS + <1 … DRS + >1 … IRS

  40. Returns To Scale • Why are returns to scale important? • If an industry faces DECREASING returns to scale, small factories make sense -It is easier to have small firms in this industry • If an industry faces INCREASING returns to scale, large factories make sense -Large firms have an advantage; natural monopolies

  41. Notes: • • The marginal product of a single factor may diminish while the returns to scale do not • Marginal product deals with a SINGLE input increasing, while returns to scale deals with MULTIPLE inputs increasing • • Returns to scale need not be the same at different levels of production

  42. 6.6 Special Production Functions • 1. Linear Production Function: • Q = aL + bK • MRTS constant • Constant returns to scale • Inputs are PERFECT SUBSTITUTES: -Ie: 10 CD’s are a perfect substitute for 1 DVD for storing data.

  43. K Example: Linear Production Function Q = Q1 Q = Q0 L 0

  44. Special Production Functions -ie: 2 pieces of bread and 1 piece of cheese make a grilled cheese sandwich: Q=min (c, 1/2b)

  45. Cheese Example: Fixed Proportion Production Function 2 Q = 2 Q = 1 1 0 Bread 2 4

  46. Special Production Functions • Cobb-Douglas Production Function: • Q = aLK • if  +  > 1 then IRTS • if  +  = 1 then CRTS • if  +  < 1 then DRTS • smooth isoquants • MRTS varies along isoquants

  47. K Example: Cobb-Douglas Production Function Q = Q1 Q = Q0 0 L

  48. Constant Elasticity of Substitution Production Function: • Q = [aL+bK]1/ • Where  = (-1)/ • if  = 0, we get Leontief case • if  = , we get linear case • if  = 1, we get the Cobb-Douglas case • General form of other functions

  49. 6.8 Technological Progress Definition:Technological progress shifts isoquants inward by allowing the firm to achieve more output from a given combination of inputs (or the same output with fewer inputs). Neutral technological progressshifts the isoquant corresponding to a given level of output inwards, but leaves the MRTSL,K unchanged along any ray from the origin

  50. Example: “neutral technological progress” K Q = 100 before Q = 100 after MRTS remains same K/L L

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