Posted by Kayla on Saturday, May 24, 2008 at 3:02pm.
Assume that preferencse are given by u(c,L) = 2*ln(c) +ln(L). The wage rate is $15 and the person has 120 hours of time available. Profits are 0. Taxes are 0. Write down two equations that describe the constraints faced by this consumer. Find an equation for the Marginal Rate of Substitution. Find the equilibrium level of consumption and leisure.

Macroeconomics  economyst, Tuesday, May 27, 2008 at 9:45am
For 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
Answer This Question
Related Questions
 math linear equations  suppose you earn 5.50/h at a bakery. From your first ...
 linear programming  A manufacturer produces two items, bookcases and library ...
 finite math  2. The Witherspoon Down Company specializes in making down ...
 Help...More Math Help!!!...Please!  A kayaker paddled 2 hours with a 6 mph ...
 Macroeconomics  Describe how each of the following will affect the equilibrium ...
 College Macroeconomics  Can someone who knows Macroeconomics check this? Write ...
 principles of macroeconomics  The following is a list of figures for a given ...
 The Graphical Method  A manufacturer produces two models of mountain bikes. ...
 Finite Math  Please help...i'm totally lost with this one. Construct a linear ...
 linear programming app  write the constraints as linear inequalities and ...
More Related Questions