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Econ100B PS5 Solutions

# Econ100B PS5 Solutions - on the contract curve where Tony...

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ECO 100B Problem Set 5 20. MRS A = Z A C A MRS S = Z S C S At points on the contract curve, Z S = 30 Z A , C S = 30 C A , and so Z A C A = 30 Z A 30 C A Z A = C A p 1 and p 2 : 5 = Q 1 = 10 2 p 1 + p 2 5 = Q 2 = 10 2 p 2 + p 1 Subtract the 2nd equation from the &rst yields 0 = 3 ( p 2 p 1 ) p 2 = p 1 5 = 10 2 p 1 + p 1 p 1 = p 2 = 5 23. First consider the equilibrium in the market for Good 1: Q D 1 = Q S 1 15 3 p 1 + p 2 = 2 + p 1 p 2 = 4 p 1 13 1

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Now consider the equilibrium in the market for Good 2: Q D 2 = Q S 2 6 2 p 2 + p 1 = 1 + p 2 p 1 = 3 p 2 5 Use the simultaneous equations in ( p 1 ;p 2 ) to solve for each: p 2 = 12 p 2 20 13 11 p 2 = 33 p 2 = 3 p 1 = 4 . Q 1 = 2 + 4 = 6 Q 2 = 1 + 3 = 4 24. We will solve for the contract curve as we did in class. Suppose we are looking for the point
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Unformatted text preview: on the contract curve where Tony receives G t units of G . Now, since the indi/erent curves have to be tangent: MRS t = MRS m & H t G t = & H 2 m 2 G m H m H t G t = H m 2 G m Now, recognize that H m = 50 & H t and G m = 100 & G t . So, H t G t = 50 & H t 2 (100 & G t ) 200 H t & 2 G t H t = 50 G t & G t H t 200 H t & G t H t = 50 G t H t = 50 G t 200 & G t So the contract curve is given by H t ( G t ) = 50 G t 200 & G t . 2...
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Econ100B PS5 Solutions - on the contract curve where Tony...

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