1. Chapter 33 Production
Key Concept: We still see the correspondence between Pareto optimum and Market Equilibrium.
Efficiency in the use of inputs
Efficiency in exchange
Efficiency in the output market

2. Chapter 33 Production
We now add production into the economy.
Two goods: fish and coconuts (F and C).
Two firms: one producing F and the other producing C.
Two inputs: L and K.

3. Consumers are endowed with factor inputs and ownership of firms (shareholders). So the profit of firms will be distributed to consumers.

4. First look at the Pareto optimum.
Efficiency in the use of inputs in production
Efficiency in exchange
Efficiency in the output market

5. Efficiency in the use of inputs in production requires that in an Edgeworth box (where the endowed labor and the endowed capital are the width and length of the box respectively), two firms’ MRTS must equal.
Suppose MRTSL,KF=2>MRTSL,KC=0.5, then one unit of L should be moved from C to F and one unit of K from F to C.
Both C and F can be increased.

7. We can plot all the points in the Edgeworth box into the plane of F-C.
We will get the production possibility set which shows the various combinations of fish and coconuts that can be produced with fixed inputs.

8. A production possibilities set.
The production possibilities set measures the set of outputs that are feasible given the technology and the amounts of inputs.

9. The production possibility frontier then corresponds to the Pareto set.
If we increase one unit of F, how many units of C do we have to decrease?

10. This is called the marginal rate of transformation.
By definition, it is ∆C/∆F.
By moving one unit of L from C to F, we increase F by MPLF and decrease C by MPLC.
Hence, MRTF,C= MPLC / MPLF.

11. Alternatively, we can move one unit of K from C to F, then we increase F by MPKF and decrease C by MPKC.
Hence, MRTF,C= MPKC / MPKF.
MRTF,C= MPLC / MPLF
MRTF,C= MPKC / MPKF

12. MRTF,C= MPLC / MPLF
MRTF,C= MPKC / MPKF
At Pareto set the isoquants are tangent to each other or
MPLC / MPKC = MPLF / MPKF
MPLC / MPLF = MPKC / MPKF, so both gives you the same MRT.

13. Efficiency in exchange still has to hold.
In other words, given F and C are produced, efficiency implies that MRSAF,C=MRSBF,C.

14. Efficiency in the output market means producers produce what consumers want.
This implies MRTF,C=MRSAF,C=MRSBF,C.

15. This implies MRTF,C=MRSAF,C=MRSBF,C.
Suppose MRTF,C=0.5<MRSAF,C=2, then we can increase F by 1 by decreasing C by 0.5.
However, this change makes consumer A strictly better off since increasing F by 1, he is willing to give up C by 2 and now the society only gives up C by 0.5.

16. Production and the Edgeworth box.
At each point on the production possibilities frontier, we can draw an Edgeworth box to illustrate the possible consumption allocations.

17. How does market achieve this?
Efficiency in the use of inputs in production is achieved because firms max profits implies they min costs.
Therefore, their isoquants are tangent to isocost. Since the isocosts of firms have the same slope. We get:
MRTSL,KF=w/r=MRTSL,KC.

18. Efficiency in exchange is achieved by the same reason as in the last chapter, i.e., MRSAF,C=pF/pC=MRSBF,C.

19. Efficiency in the output market is achieved because when each firm (say firm F) max profit, it chooses
pF MPLF=w and pC MPLC=w. This implies
MRTF,C= MPLC/MPLF= pF/pC. Since
MRSAF,C=pF/pC=MRSBF,C, so MRT=MRS.

20. hours of labor required to produce
Cheese (1 lb)
Wine (1 gal)
Holland
1 (1/2W*)
2 (2C)
Italy
6 (2W)
3 (1/2 C*)

21. In each box, we have the hours of labor required to produce a certain amount of output.
We can draw the production possibility frontier of each country.
Now what is the production frontier of the world?

22. Now what is the production frontier of the world?
To produce the first unit of C, should ask Holland to produce. Up to the point where all the labor of Holland has been employed to produce C.
Mention international trade.

23. Mention the Walras’ law.
F= pF F-wLF-rKF and C= pC C-wLC-rKC.
pFxFA+pCxCA=wLA+rKA+ θ FF + θCC and. pFxFB+pCxCB=wLB+rKB+(1-θF)F +(1- θC)C.
Adding these up, we get pF(xFA+xFB-F)+pC(xCA+xCB-C)+w(LF+LC-LA-LB)+r(KF+KC-KA-KB)+F-(θFF+(1-θF)F)+C-(θCC+(1-θC)C)=0.

24. To summarize:
Efficiency in exchange: MRSAF,C=pF/pC=MRSBF,C.
Efficiency in the use of inputs in production: MRTSL,KF=w/r=MRTSL,KC.
Efficiency in the output market: MRTF,C= MPLC/MPLF= pF/pC = MRSAF,C.

25. Chapter 33 Production
Key Concept: We still see the correspondence between Pareto optimum and Market Equilibrium.
Efficiency in the use of inputs
Efficiency in exchange
Efficiency in the output market