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January 29, 2015

January 29, 2015

Posted by **Kayla** on Saturday, May 24, 2008 at 3:02pm.

- Macroeconomics -
**economyst**, Tuesday, May 27, 2008 at 9:45amFor convenience, let c= $15 of consumption. (Dont worry, you would get the same answer if c=$1 of consumption)

So, your equations are:

Max(U)=2*ln(c)+ln(L)

subject to:

c+L=120

To get one L,the person must give up one c. So the price of L in terms of C is 1. Soooooo, we want the marginal rate of substitution in utility to be equal to ratio of prices of L and c

So, next take the partial derivitives MU(c) and MU(L). These are 2/c and 1/L.

The marginal rate of substitution is MU(L)/MU(c) = (1/L)/(2/c) = c/2L

To maximize c/2L = 1 or c=2L, subject to c+L=120.

c=80, L=40

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