1. Producer Theory Tutorial 6

2. Page 2 The Production Functions  Firms -A firm is an organization that turns inputs into outputs. -The major assumption: Profit maximization -where TR = P x Q is the total revenue; TC is the total cost of production -Two decisions: Input Choice: Choose the input that will minimize cost to produce any given output. Output Choice: Choose the amount of output produced and hence the price of the product.

3. Page 3 Production Function  Production function: shows the relationship between the maximum amount of output a firm can produce and the amount inputs used, given the current technology. where L is the quantity of labor used; K is the quantity of capital used.  The production function can be represented in a 3-D diagram.

4. Page 4 The Production Functions 0 L K Q L1L1 Keep K constant L2L2 K1K1

5. Page 5 Short-run Production  Input flexibility -Short run: a period of time that at least one factor of production is fixed, i.e. the fixed input. -Long run: a period of time, which is long enough that all inputs can be variable. How long does it take for all inputs to be variable?  Short-run production: One variable Input -In the short run, economists usually assume that capital is fixed. -If we were to cut the hill vertically at a particular level of K, we can study how output level varies with the change in L, keeping K constant.

6. Page 6 Q L Q1Q1 A 0 L1L1 TP L Q2Q2 L2L2 B ΔQΔQ ΔLΔL Law of diminishing marginal returns: If a firm increases an input successively, keeping all other inputs constant, the marginal product of the variable input will eventually diminish.  Marginal product of labor (MP L ): the additional output that can be produced by employing one more unit of labor, keeping the amount of capital used constant. Total Product Curve

7. Page 7 Q L Q L AP L MP L L2L2 L3L3 L1L1 L4L4 Q1Q1 A B C D AP L1 = Q 1 /L 1 MP L1 0 b c d Average product of labor (AP L ): the average amount of output per unit of labor

8. Page 8 Long-run Production: Isoquants  In the long run, both K and L are variable. A firm, therefore, is possible to produce a particular output level with different combinations of inputs.  If we were to cut the hill horizontally at a particular level of output, and project the outside edge of the hill on the floor. We derive a curve that shows all the combinations of labor and capital that can be used to produce the same level of output. This is called the isoquant. 0 L K Q Q1Q1 Q2Q2

9. Page 9 Contour Lines

10. Page 10 Isoquants  Isoquant map: a graphical representation of a set of isoquants. L K L2L2 K1K1 L1L1 K1K1 b a

11. Page 11 Isocost Lines  The total cost of production is the sum of the labor cost and capital cost:  Isocost Line: It shows all the combinations of inputs that incur the same cost for the firm. K IL L  Derive another isocost line that represents a lower total cost.  Suppose the wage rate increases, with the rental price of capital remains unchanged. Derive the isocost line that represents the same total cost.

12. Page 12 The Firm’s Optimal Input Choice  A consumer’s optimal choice is the input combination that minimizes its total cost to produce a given output level. -Put the isoquant curves and isocost line together!

13. Page 13 Firm Optimal Choice Q1Q1 E C D A B L K IL 2  Which point is the firm’s optimal input choice? -Must lie on the isoquant -The point where the isoquant is tangent to the lowest attainable isocost line. IL 1

14. Page 14 Application: Minimum Wage in Shenzhen  “Shenzhen Municipal Government raised the minimum wage by 17.6% starting 1 July, 2008. (Source: Hong Kong Economic Times, 26 June, 2008)

15. Page 15 Comparative Statics Analysis: Changes in Input Prices  Suppose wage rate increases from w 1 to w 2.  The firm will substitute capital for labor to produce Q 1, so as to reduce the costs.  Change in cost?  What if the firm do not change its input combination? L K IC 2 IC 1 Q1Q1 IC 3 E1E1 E2E2

16. Page 16 Discussion Question 1: Minimum Wage in Shenzhen  “Shenzhen Municipal Government raised the minimum wage by 17.6% starting 1 July, 2008. (Source: Hong Kong Economic Times, 26 June, 2008)  Hong Kong factories decided to install more machines to automate simple production procedures (replacing low-skilled labor) in order to cut costs”

17. Page 17 Application: Nothing to Lose but their Chains (Source: “Nothing to lose but their chains,” The Economist, 21 st June 2008. ) -“… Some factory robots are now smart enough top be released from their safety cages to work among humans. And as they become cleverer and more dexterous, they are starting to move from factories to offices and homes …” -“…Eventually, advanced humanoid robots will escape from the laboratory. Indeed, Toyota and Honda expect domestic robots to become a huge market in the future, with machines working as a family helper.” -“… Four trends were on show: robots are rapidly becoming more responsive, cheaper, simpler to program and safer…”

18. Page 18 Discussion Question 3  What is the difference between decreasing returns to scale and diminishing marginal returns? Can a production function exhibit diminishing marginal returns but not decreasing returns to scale?  Returns to scale: to measure how output responds to increases in all inputs together.  If the production function is given by and all inputs are multiplied by the same positive constant, e.g. 2, we describe the returns to scale of the production function: -Constant returns to scale: -Increasing returns to scale: -Decreasing returns to scale:

19. Page 19 Returns to Scale L K K 2K 2LL q 2q 3q L K K 2K 2LL q L K K 2K 2LL q 2q 3q 2q Increasing Returns to Scale Constant Returns to Scale Decreasing Returns to Scale

20. Page 20 Returns to Scale  Note that decreasing returns to scale is different from the diminishing marginal returns. L q = 500 A B C D K q=650 q=750 q=1000 q=1500 E 1 2 3 123

21. Page 21 Discussion Question 4  Suppose the firm wants to increase its output level in the short run, compare its optimal input choice in the short run and long run. L Q3Q3 e1e1 K Q1Q1 Q2Q2 e3e3 e2e2 e4e4 e 5  Short-run cost will never be lower than the long-run cost!