Economics help! In an economy with 16lbs of cheese and 20 bottles of wine Alice

Question

Economics help! In an economy with 16lbs of cheese and 20 bottles of wine Alice and bills utility functions are Ua=2w+C Ub=W+2C
Alice has 10lbs of cheese and 12 bottles of wine while bill has 6lbs of cheese and 8 bottles of wine Is this an efficient allocation? If no find a Preto superior allocation. Indicate the contract curve Economics help! In an economy with 16lbs of cheese and 20 bottles of wine Alice and bills utility functions are Ua=2w+C Ub=W+2C
Alice has 10lbs of cheese and 12 bottles of wine while bill has 6lbs of cheese and 8 bottles of wine Is this an efficient allocation? If no find a Preto superior allocation. Indicate the contract curve Economics help! In an economy with 16lbs of cheese and 20 bottles of wine Alice and bills utility functions are Ua=2w+C Ub=W+2C
Alice has 10lbs of cheese and 12 bottles of wine while bill has 6lbs of cheese and 8 bottles of wine Is this an efficient allocation? If no find a Preto superior allocation. Indicate the contract curve Economics help! In an economy with 16lbs of cheese and 20 bottles of wine Alice and bills utility functions are Ua=2w+C Ub=W+2C
Alice has 10lbs of cheese and 12 bottles of wine while bill has 6lbs of cheese and 8 bottles of wine Is this an efficient allocation? If no find a Preto superior allocation. Indicate the contract curve In an economy with 16lbs of cheese and 20 bottles of wine Alice and bills utility functions are Ua=2w+C Ub=W+2C
Alice has 10lbs of cheese and 12 bottles of wine while bill has 6lbs of cheese and 8 bottles of wine Is this an efficient allocation? If no find a Preto superior allocation. Indicate the contract curve

Explanation / Answer

Ua = 2w+c

Ub = w+2c

For Pareto efficiency, the two MRS of both individual should be equal.

MRS of alice : MRS = wine/cheese = 12/10 = 1.2

and MRS of bill = wine/cheese = 8/6 = 1.33

as 1.2 is not equal to 1.33, this allocation is not an effecient allocation.

To get optimal allocation we requires,

Wa/Ca = Wb/Cb ...... eq 1

And

W = Wa +Wb = 20

and C = Ca+Cb = 16

thus Wa/Ca = 20-Wa / 16-Ca

Wa(16-Ca) = Ca(20-Wa)

16Wa - WaCa = 20Ca - WaCa

Wa = 1.25Ca

and from equation i

1.25Ca/Ca = Wb/Cb

Wb = 1.25 Cb

Ua = 2(1.25C) + C = 3.5 C

and Ub = 1.25C + 2C = 3.25C

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