# Macroeconomics

posted by .

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 -

For convenience, let c= \$15 of consumption. (Dont worry, you would get the same answer if c=\$1 of consumption)

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

## Similar Questions

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water. The speed is 6 mph slower going upstream and 6 mph faster going …
2. ### math linear equations

suppose you earn 5.50/h at a bakery. From your first paycheck you discover that \$1.15/h is withheld for taxes and benefits. you work x hours in a five day week and you spend \$3.75 each day on lunch. Write an equationfor your earnings …
3. ### Finite Math

Please help...i'm totally lost with this one. Construct a linear program for the following situation. Do not solve. A hotel is refurbishing its rooms, each type of which will accommodate either one or two persons. A one-person room …
4. ### College Macroeconomics

Can someone who knows Macroeconomics check this?
5. ### linear programming app

write the constraints as linear inequalities and identify all variables used. A canoe requires 8 hours of fabrication and a rowboat 5 hours. The fabrication department has at most 110 hours of labor available each week
6. ### linear programming

A manufacturer produces two items, bookcases and library tables. Each item requires processing in each of two departments. Department I has 40 hours available and department II has 36 hours available each week for production. To manufacture …
7. ### finite math

2. The Witherspoon Down Company specializes in making down jackets, ski vests, and comforters. The requirements for down and labor and the profits earned are given in the following chart: Down (pounds) Time (labor-hours) Profit (\$) …
8. ### Macroeconomics

Describe how each of the following will affect the equilibrium price level(P) and real output(Y) in the short run(Assume the economy is initially in the long-run equilibrium.) (a) A reduction in the real interest rate (b) A widespread …
9. ### principles of macroeconomics

The following is a list of figures for a given year in billions of dollars. Using this data, compute: (a) GDP; (b) NDP; (c) NI; (d) PI; (e) DI; (f) Net exports. Transfer payments \$ 16 Government purchases 80 Personal taxes 38 Corporate …
10. ### The Graphical Method

A manufacturer produces two models of mountain bikes. Model A requires 5 hours of assembly time and 2 hours of painting time, and Model B requires 4 hours of assembly time and 3 hours of painting time. The maximum total weekly hours …

More Similar Questions