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Kate and Humphrey have initial endowments of goods 1 and 2, eL = (8, 2) and...

Kate and Humphrey have initial endowments of goods 1 and 2, eL = (8, 2) and eH = (2, 8). Kate’s preferences are represented by utility function uL(x1,x2) = x1x2 and Humphrey’s preferences are represented by utility function uH (x1, x2) = ((x1)^2)(x2). Denote by xL = (x1L , x2L) Lauren’s equilibrium consumption bundle. Humphrey’s consumption bundle is xH = (x1H ,x2H ). In equilibrium it must that x1L +x1H = e1L +e1H = 10 and x2L +x2H = e2L+e2H = 2+8 = 10. Determine all equlibrium allocations, (xL, xH ) that are on the contract curve.

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