Chapter Thirty-Two Production

Exchange Economies (revisited)  No production, only endowments, so no description of how resources are converted to consumables.  General equilibrium: all markets clear simultaneously.  1st and 2nd Fundamental Theorems of Welfare Economics.

Now Add Production...  Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits …

Now Add Production...  Add input markets, output markets, describe firms’ technologies, the distributions of firms’ outputs and profits … That’s not easy!

Robinson Crusoe’s Economy  One agent, RC.  Endowed with a fixed quantity of one resource hours.  Use time for labor (production) or leisure (consumption).  Labor time = L. Leisure time = 24 - L.  What will RC choose?

Robinson Crusoe’s Technology  Technology: Labor produces output (coconuts) according to a concave production function.

Robinson Crusoe’s Technology Production function Labor (hours) Coconuts 24 0

Robinson Crusoe’s Technology Labor (hours) Coconuts Production function 24 0 Feasible production plans

Robinson Crusoe’s Preferences  RC’s preferences:  coconut is a good  leisure is a good

Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 24 0

Robinson Crusoe’s Preferences Leisure (hours) Coconuts More preferred 240

Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0

Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

Robinson Crusoe’s Choice Labor (hours) Coconuts Feasible production plans Production function 24 0 Leisure (hours) 240

Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L*

Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* Labor

Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure

Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure Output

Robinson Crusoe’s Choice Labor (hours) Coconuts Production function 24 0 Leisure (hours) 240 C* L* LaborLeisure MRS = MP L Output

Robinson Crusoe as a Firm  Now suppose RC is both a utility-maximizing consumer and a profit-maximizing firm.  Use coconuts as the numeraire good; i.e. price of a coconut = $1.  RC’s wage rate is w.  Coconut output level is C.

Robinson Crusoe as a Firm  RC’s firm’s profit is  = C - wL.   = C - wL  C =  + wL, the equation of an isoprofit line.  Slope = + w.  Intercept = .

Isoprofit Lines Labor (hours) Coconuts 24 Higher profit; Slopes = + w 0

Profit-Maximization Labor (hours) Coconuts Feasible production plans Production function 24 0

Profit-Maximization Labor (hours) Coconuts Production function 24 0

Profit-Maximization Labor (hours) Coconuts Production function 24 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. RC gets 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. Given w, RC’s firm’s quantity demanded of labor is L* Labor demand RC gets 0

Profit-Maximization Labor (hours) Coconuts Production function 24 C* L* Isoprofit slope = production function slope i.e. w = MP L = 1  MP L = MRP L. Given w, RC’s firm’s quantity demanded of labor is L* and output quantity supplied is C*. Labor demand Output supply RC gets 0

Utility-Maximization  Now consider RC as a consumer endowed with $  * who can work for $ w per hour.  What is RC’s most preferred consumption bundle?  Budget constraint is

Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint

Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

Utility-Maximization Labor (hours) Coconuts More preferred 24 0

Utility-Maximization Labor (hours) Coconuts 24 0 Budget constraint; slope = w

Utility-Maximization Labor (hours) Coconuts Budget constraint; slope = w 24 0

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Budget constraint; slope = w

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* MRS = w Budget constraint; slope = w

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Labor supply Budget constraint; slope = w MRS = w Given w, RC’s quantity supplied of labor is L*

Utility-Maximization Labor (hours) Coconuts 24 0 C* L* Given w, RC’s quantity supplied of labor is L* and output quantity demanded is C*. Labor supply Output demand Budget constraint; slope = w MRS = w

Utility-Maximization & Profit- Maximization  Profit-maximization:  w = MP L  quantity of output supplied = C*  quantity of labor demanded = L*

Utility-Maximization & Profit- Maximization  Profit-maximization:  w = MP L  quantity of output supplied = C*  quantity of labor demanded = L*  Utility-maximization:  w = MRS  quantity of output demanded = C*  quantity of labor supplied = L*

Utility-Maximization & Profit- Maximization  Profit-maximization:  w = MP L  quantity of output supplied = C*  quantity of labor demanded = L*  Utility-maximization:  w = MRS  quantity of output demanded = C*  quantity of labor supplied = L* Coconut and labor markets both clear.

Utility-Maximization & Profit- Maximization Labor (hours) Coconuts 24 C* L* 0 MRS = w = MP L Given w, RC’s quantity supplied of labor = quantity demanded of labor = L* and output quantity demanded = output quantity supplied = C*.

Pareto Efficiency  Must have MRS = MP L.

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS  MP L Preferred consumption bundles.

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L

Pareto Efficiency Labor (hours) Coconuts 24 0 MRS = MP L. The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

First Fundamental Theorem of Welfare Economics  A competitive market equilibrium is Pareto efficient if  consumers’ preferences are convex  there are no externalities in consumption or production.

Second Fundamental Theorem of Welfare Economics  Any Pareto efficient economic state can be achieved as a competitive market equilibrium if  consumers’ preferences are convex  firms’ technologies are convex  there are no externalities in consumption or production.

Non-Convex Technologies  Do the Welfare Theorems hold if firms have non- convex technologies?

Non-Convex Technologies  Do the Welfare Theorems hold if firms have non- convex technologies?  The 1st Theorem does not rely upon firms’ technologies being convex.

Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L The common slope  relative wage rate w that implements the Pareto efficient plan by decentralized pricing.

Non-Convex Technologies  Do the Welfare Theorems hold if firms have non- convex technologies?  The 2nd Theorem does require that firms’ technologies be convex.

Non-Convex Technologies Labor (hours) Coconuts 24 0 MRS = MP L. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.

Production Possibilities  Resource and technological limitations restrict what an economy can produce.  The set of all feasible output bundles is the economy’s production possibility set.  The set’s outer boundary is the production possibility frontier.

Production Possibilities Fish Coconuts Production possibility frontier (ppf)

Production Possibilities Fish Coconuts Production possibility frontier (ppf) Production possibility set

Production Possibilities Fish Coconuts Feasible but inefficient

Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient

Production Possibilities Fish Coconuts Feasible but inefficient Feasible and efficient Infeasible

Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation.

Production Possibilities Fish Coconuts Ppf’s slope is the marginal rate of product transformation. Increasingly negative MRPT  increasing opportunity cost to specialization.

Production Possibilities  If there are no production externalities then a ppf will be concave w.r.t. the origin.  Why?

Production Possibilities  If there are no production externalities then a ppf will be concave w.r.t. the origin.  Why?  Because efficient production requires exploitation of comparative advantages.

Imagine an economic system with only two goods, potatoes and meat and only two people, a potato farmer and a cattle rancher  What should each person produce?  Why should these people trade? A PARABLE FOR THE MODERN ECONOMY

Production Possibilities  Suppose the farmer and rancher decide not to engage in trade:  Each consumes only what he or she can produce alone.  The production possibilities frontier is also the consumption possibilities frontier.  Without trade, economic gains are diminished.

Figure 1 The Production Possibilities Frontier Potatoes (ounces) A 0 Meat (ounces) (a) The Farmer’s Production Possibilities Frontier If there is no trade, the farmer chooses this production and consumption. Copyright©2003 Southwestern/Thomson Learning

Figure 1 The Production Possibilities Curve Copyright©2003 Southwestern/Thomson Learning Potatoes (ounces) B 0 Meat (ounces) (b) The Rancher’s Production Possibilities Frontier If there is no trade, the rancher chooses this production and consumption.

Production and Consumption Without Trade

The farmer should produce potatoes. The rancher should produce meat. Specialization and Trade  Suppose instead the farmer and the rancher decide to specialize and trade…  Both would be better off if they specialize in producing the product they are more suited to produce, and then trade with each other.

Figure 2 How Trade Expands the Set of Consumption Opportunities Copyright©2003 Southwestern/Thomson Learning Potatoes (ounces) A A* 0 Meat (ounces) (a) The Farmer’s Production and Consumption Farmer's production and consumption without trade Farmer's consumption with trade Farmer's production with trade

Figure 2 How Trade Expands the Set of Consumption Opportunities Copyright © 2004 South-Western Potatoes (ounces) B 0 Meat (ounces) (b) The Rancher’s Production and Consumption B* Rancher's consumption with trade Rancher's production with trade Rancher's production and consumption without trade

COMPARATIVE ADVANTAGE  Differences in the costs of production determine the following:  Who should produce what?  How much should be traded for each product?

COMPARATIVE ADVANTAGE  Two ways to measure differences in costs of production:  The number of hours required to produce a unit of output (for example, one pound of potatoes).  The opportunity cost of sacrificing one good for another.

Comparative Advantage and Trade  Potato costs…  The Rancher’s opportunity cost of an ounce of potatoes is 1/2 an ounce of meat.  The Farmer’s opportunity cost of an ounce of potatoes is1/4 an ounce of meat.  Meat costs…  The Rancher’s opportunity cost of a pound of meat is only 2 ounces of potatoes.  The Farmer’s opportunity cost of an ounce of meat is only 4 ounces of potatoes...

Comparative Advantage and Trade …so, the Rancher has a comparative advantage in the production of meat but the Farmer has a comparative advantage in the production of potatoes.

Comparative Advantage and Trade  Comparative advantage and differences in opportunity costs are the basis for specialized production and trade.  Whenever potential trading parties have differences in opportunity costs, they can each benefit from trade.

Gains from Trade

Comparative Advantage and Trade  Benefits of Trade  Trade can benefit everyone in a society because it allows people to specialize in activities in which they have a comparative advantage.

Comparative Advantage  Two agents, RC and Man Friday (MF).  RC can produce at most 20 coconuts or 30 fish.  MF can produce at most 50 coconuts or 25 fish.

Comparative Advantage F C F C RC MF

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts.

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts.

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more fish is 2/3 foregone coconuts. MRPT = -2 coconuts/fish so opp. cost of one more fish is 2 foregone coconuts. RC has the comparative opp. cost advantage in producing fish.

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish.

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish.

Comparative Advantage F C F C RC MF MRPT = -2/3 coconuts/fish so opp. cost of one more coconut is 3/2 foregone fish. MRPT = -2 coconuts/fish so opp. cost of one more coconut is 1/2 foregone fish. MF has the comparative opp. cost advantage in producing coconuts.

Comparative Advantage F C Economy F C F C RC MF Use RC to produce fish before using MF. Use MF to produce coconuts before using RC.

Comparative Advantage F C Economy F C F C RC MF Using low opp. cost producers first results in a ppf that is concave w.r.t the origin.

Comparative Advantage F C Economy More producers with different opp. costs “smooth out” the ppf.

Coordinating Production & Consumption  The ppf contains many technically efficient output bundles.  Which are Pareto efficient for consumers?

Coordinating Production & Consumption Fish Coconuts Output bundle is

Coordinating Production & Consumption Fish Coconuts Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

Coordinating Production & Consumption Fish Coconuts O RC O MF Output bundle is and is the aggregate endowment for distribution to consumers RC and MF.

Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC

Coordinating Production & Consumption Fish Coconuts O RC O MF Allocate efficiently; say to RC and to MF.

Coordinating Production & Consumption Fish Coconuts O RC O MF

Coordinating Production & Consumption Fish Coconuts O RC O MF

Coordinating Production & Consumption Fish Coconuts O RC O MF

Coordinating Production & Consumption Fish Coconuts O RC O MF MRS  MRPT

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before.

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged.

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher

Coordinating Production & Consumption Fish Coconuts O RC O MF O’ MF Instead produce Give MF same allocation as before. MF’s utility is unchanged, RC’s utility is higher; Pareto improvement.

Coordinating Production & Consumption  MRS  MRPT  inefficient coordination of production and consumption.  Hence, MRS = MRPT is necessary for a Pareto optimal economic state.

Coordinating Production & Consumption Fish Coconuts O RC O MF

Decentralized Coordination of Production & Consumption  RC and MF jointly run a firm producing coconuts and fish.  RC and MF are also consumers who can sell labor.  Price of coconut = p C.  Price of fish = p F.  RC’s wage rate = w RC.  MF’s wage rate = w MF.

Decentralized Coordination of Production & Consumption  L RC, L MF are amounts of labor purchased from RC and MF.  Firm’s profit-maximization problem is choose C, F, L RC and L MF to

Decentralized Coordination of Production & Consumption Isoprofit line equation is

Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

Decentralized Coordination of Production & Consumption Isoprofit line equation is which rearranges to

Decentralized Coordination of Production & Consumption Fish Coconuts Higher profit Slopes =

Decentralized Coordination of Production & Consumption Fish Coconuts The firm’s production possibility set.

Decentralized Coordination of Production & Consumption Fish Coconuts Slopes =

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slopes =

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope =

Decentralized Coordination of Production & Consumption Fish Coconuts Profit-max. plan Slope = Competitive markets and profit-maximization 

Decentralized Coordination of Production & Consumption  So competitive markets, profit-maximization, and utility maximization all together cause the condition necessary for a Pareto optimal economic state.

Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets and utility-maximization 

Decentralized Coordination of Production & Consumption Fish Coconuts O RC O MF Competitive markets, utility- maximization and profit- maximization 