Production Problem Set

Department of Economics                                                                Economics 3501

 

NAME

A. Cookies

1. SmartTough is a commercial bakery selling cookies over the internet. The following table provides someinformation about cookie production at the bakery. Fill in the table below.

Bakers [L] Tons of Cookies [Q] Average Product [AP(L)] Marginal Product [MP(L)]
0 0 **** ****
1 15 15 15
2 36 18 21
3 56 18.67 20
4 72 18 16
5 82 82/5=16.4 10
6 84 14 2

2.  After what unit of labor do diminishing marginal returns set in? 2 or 3

3. When a firm is experiencing diminishing marginal returns, average product must be declining. True   False

4. The main reason SmartTough.com experiences diminishing returns is that as it increases its hiring it is forced to hire less productive workers.   True  False

B. Fruit

The Pitcairn Islands produce peaches and plums using only labor.  The annual labor supply is 10 person-years.  The production schedules for the two goods are shown below.

Labor Peaches Labor Plums
0 0 0 0
2 50 2 20
4 90 4 38
6 120 6 54
8 140 8 68
10 150 10 80

5. Peach production exhibits diminishing marginal returns. True False

6. Plum production exhibits diminishing marginal returns.  True  False

7. At what level of peach production are average and marginal product equal? 50

8. At what level of plum production are average and marginal product equal? 20

9. If the islanders have chosen to produce 120 peaches, how many plums can they produce? 38

10. When producing 90 peaches, what is the opportunity cost of producing 30 more peaches? 16

C. Wood Products

Papyrus Products Corporation produces fiberboard using sawdust and hydraulic presses.  PPC's daily production (measured in tons) is illustrated in the table below.  Output varies with different combinations of the quantity of sawdust and machines.

   

Sawdust
    0 1 2 3

Machines

 0 0 0 0 0
1 0 0.5 0.9 1.2
2 0 0.8 1.4 1.9
3 0 1.0 1.8 2.3

11.  In 2009 Papyrus owned one machine.  On March 23 of that year they processed one ton of sawdust.  How much fiberboard did they make? 0.5

12. On March 23, 2009 what was the marginal product of an additional ton of sawdust? 0.4

13. On March 23, 2009 Papyrus acquired a second press.  If they processed two tons of sawdust, what was the marginal product of the second press? 0.5

14. Papyrus' production process exhibits diminishing marginal returns to sawdust. True   False

15. Papyrus' production process exhibit constant returns to scale. True  False

D. Fish

Neptune Long Line Fishing Company uses hooks (H), lines (L) and sinkers (S) to catch anchovies (Q). Its daily production function is Q = 100H + 40L + 10 S.

16. On May 9, 2008 it used 8 hooks, 4 lines and 4 sinkers.  How many anchovies did it catch? 1000

17. What is the marginal product of an additional hook? 100

18. What is the marginal product of an additional sinker? 10

19. Does Neptune's production function exhibit  diminishing, constant or  increasing returns to scale?