Question

1. Anna’s demand for peaches is given by P_A = 200 – 3Q_A, where Q_A is the quantity (kilograms) demanded at price P_A($/kilo). Basil’s demand is given by P_B = 120 – 2Q_B, where Q_B is the quantity (kilograms) demanded at price P_B ($/kilo). Each of the two has $2,000 that they can spend if they want to buy something.
   
   1. Suppose the endowments are as follows: Anna has 110 kilograms of peaches, Basil has none. When they trade, who will sell to whom? How many kilos will be sold? At what price?
      
   2. Suppose the endowments are as follows: Anna has no peaches, Basil has 110 kilos. When they trade, who will sell to whom? How many kilos will be sold? At what price?
      
   3. Suppose the endowments are as follows: Anna has 60 kilograms of peaches, Basil has 50 kilos. When they trade, who will sell to whom? How many kilos will be sold? At what price?

Answer 1

demamd PA 200-39A Apmna's 200-PA demand Basil 's P=120-20B R 60-PB 2 niome Ama (MA)= 2000 Income Rasl (MB) 2000 1s Endocoment of Anna lo Endouoment Basil aut euilibium tote After tuade is allowed, al getg both people odemomd toill be esual totol deueapes and pmce faced by botth endowment the wllbe egual imdividuals 2 a 110+0 A+9B 3 ndua PR P 2Jit, 82 2 8 We get Peldbng amd S e 200 60-PR PA (s 3 r Hak PA-PRP Go -PA -Pg 3 Q 20+ 12 760-SP Fam3) we get 760-P 660 760-SP Ilo = SP= 100 6 P- 20

Ph PR P20 Loth mdnidualy Prce foced Demomd by each peiso QA 5 3 200 20 60 20 S0 1I0 endonment , She Snce eAnna ha and Ranl would Luy Anna Basil's mcome r00 0 SD X20 gloo0 money Spent ay Tasil= which u wel with in th Budget conant So, -at eulikrim Anna (onsumes 60 and Ral Cosume price 20 50 Kilo at oill sell S0 ilos to Rael at pice $20 Arma enly total enmdooment w see if we see we have wed Hee mattes tota tonl endouoment and eualled it to demand. 1t WOnld mot have matteued if the ndoomenty mdivduals wre dftuent as totel endaoment a eyal. as

tndooment of Anna o 20 Endowmeut of Basil110 TOel endowmnt 10 to tio d r To endosmend TO ta demomd &A taR= g Fom paut ca) oe get Q 380 She SP fromyout Ca) We get P $20 amd shg QA= 66 and Rso rlt AS wr notd, ny totad edowmet matfey 1sthr hono much. Mot oho owns Co whethe Anna can 3tshoba we hane to Check whlw aftret Surme 200 215/m Anna Anna bstlo pory Spent by ce $20 $1200 C 92000 ahshel Rudçet Cobant So afte bede, Bas Sells 6 kilos t Anna at ed price $20 Arma 60 endovoment F nt endowment of Basil SD TOto endonmrent = afte tmdi, Then Pa-PP 110 QA t8R 110 = 100 SP

Tuis condihon is exactly same au it uay m paut a So, after. trede pce amd quanhty grver by pautCa)-e are Theke an eractly the endoomen ty of Anna amd trdu happms anc) Bas1 each Cf o Lonsume theis endaoment thery trade happens No So, we onclude that omhy totendowmnt 1f tot endoloment mattes 込 enal, i1 be Same Quanhty thay Quom hH the afty tde they Cam afforo the au long as ro Consume, 4 3J u hant had pHo - o3 -l