1. Chapter 7 The cost of production(1) Definition of cost Short-run and long-run cost curves. Cost minimization Production with two outputs — economies of scope

2. 7.1.1 Different kinds of cost Accounting cost:actual expenses plus depreciation of capital equipment. Economic cost:accounting cost plus self-owned factor ’ s opportunity cost. Opportunity cost:the highest possible returns you forgo when you choose from different kinds of utilization ways. (the opportunity cost of going to the cinema is very high in examination days) The difference between accounting cost and economic cost.The difference between accounting cost and economic cost. Sunk cost:expenditure that has been made and cannot be recovered. It has strategic commitment role in a game. (break the kettle and sink the boat, free producing capacity) Fixed cost and sunk cost: irrecoverable part of fixed cost is sunk cost. Fixed cost=sunk cost (irrecoverable fixed cost) +recoverable fixed cost.(rent for a year which permit the renter to transfer the contract, a building with the name of its owner engraved on the wall).

3. Costs in the short run In the short run,at least one kind of inputs is fixed. Total cost definition function: TC=FC+VC(Q), usually TC increase with Q. Marginal cost:the increase in cost that results from producing one extra unit of output. It ’ s easy to prove that MVC(Q)=MC(Q) MC(Q)=C(Q+1)-C(Q) MC(Q)=[C(Q+K)-C(Q)]/K, when K is infinitely small, MC(Q)=C ’ (Q). The product should be theoretically infinitely divisible here. Average total cost and average variable cost,average fixed cost:ATC=TC(Q)/Q,AVC=VC(Q)/Q,AFC(Q)=FC/Q.

4. An example TC(Q)=Q 3 /3-10Q 2 +100Q+4000 VC(Q)= Q 3 /3-10Q 2 +100Q FC(Q)=4000 MC(Q)=Q 2 -20Q+100=MVC(Q) ATC(Q)=Q 2 /3-10Q+100+4000/Q AVC(Q) =Q 2 /3-10Q+100

5. 7.1.3 Marginal cost and the marginal returns are changing oppositely---the shape of marginal cost curve. Diminishing marginal returns implies increasing marginal cost.The proving process is as flowing: MC=dTC(Q)/dQ C=Kr+wL In short run,K is a fixed amount and w and r are given. MC(Q)=w dL/dQ Conclusion:, Then MP L eventually decreasing implies MC eventually increasing. MC(Q)=w/MP L

6. 7.2 The shapes of the cost curves The member of cost curves family: TC,FC,VC,ATC,AVC,AFC,MC(MVC). MC and ATC,AVC:First, MC, ATC,AVC are all U-shape curves.Second,MC passing through ATC and AVC’s minimization point.Third, ATC and AVC will intersect at the infinite faraway point. Forth, MC and AVC will intersect at a certain point on the vertical axis. TC and ATC.TC and MC.(two special points on TC---inflexion point and a special tangent passing through original point )Pg.211.Figure7-1. TC and VC,FC: TC(Q) =VC(Q)+FC(Q) ATC and AVC,AFC:ATC(Q) = AVC(Q)+AFC(Q) AVC(0)=MC(0)

7. TC VC MC AVC ATC Q Q MC AVC ATC FC Q 1 Q 2 Q 3 A B C O

8. Cost in the long run In the long run,the firm can change all its inputs,which means K and L are both variables,in contrast to the short run question---only the labor input amount is variable. 1 Isocost line and its change 2 Cost minimization and its condition. 3 Long-run cost function: the relationship between lowest long-run cost and the level of output. Long- run cost is always lower than short-run cost.

9. 7.3.1 The isocost line ( The pivot and shift of the budge constraint line ) Isocost line:all possible combination of labor and capital that can be purchased for a given total cost.(it sounds like the budge constraint line) The equation for a typical isocost line: wL+rK=C 0, The isocost line divide the plane into two parts. Rewrite it to get:K=C/r--(w/r)L. (slope and vertical intercept) Relative price change cause the isocost line to pivot around one extreme point. Different cost at the same relative prices just means the shift up and down of the isocost line.

10. 7.3.2 Producing a given output at a minimum cost The cost minimization decision:for a given amount of output(a given isoquant), try to find the lowest isocost line the isoquant can touch. At the optimal point,the isoquant is tangent to the isocost line. Q1Q1 A L K Q2Q2 B C

11. 7.3.2 The optimal inputs condition The isoquant’s slope is dK/dL=-MRTS LK =-MP L /MP K. The isocost line’s slope is relative price of inputs: dK/dL=-w/r. So the optimal inputs condition is : MP L /MP K =w/r. (relative marginal returns of labor equals to relative marginal cost of labor). Or rewrite it to get MP L /w=MP K /r.It’s another way to express each last unit of money should get the same productivity(utility). Why the developed country use more capital to substitute labor compared with the developing country ? Pg.219,Figure 7.4)

12. Summary Different kinds of cost. Marginal cost increasing and marginal product decreasing. The shape of cost curves:TC.FC.VC.AFC.AVC.ATC.MC Isocost line Optimal input condition: MP L /MP K =w/r. or more generally