looking for someone to solve these questions. #LABOR ECONOMICS 1.

looking for someone to solve these questions.

#LABOR ECONOMICS

1. Shelly’s preference for consumption and leisure can be expressed as

U(C,L) = C * (L-20)

There are 120 hours in the week available to split between work and leisure. Shelly earns \$ 10 per hour after taxes. She also receives \$ 500 worth of benefits each week regardless of how much she works.

a) Graph Shelly’s budget line

b) What is Shelly’s marginal rate of substitution when L=100 and she is on her budget line?

c) What is Shell’s reservation wage?

d) Find Shelly’s optimal amount of consumption and leisure

e) Derive the formula that C/L = -(MUX= MUC)

2. A firm faces the following inverse demand curve

P= 54-0.5Q

Where P is the price of output and Q is the number of outputs sold per hour. This firm is the only employer in town and faces an hourly supply of labor given by:

W=0.5E +10

Where w is the hourly wage rate and E is the number of workers hired each hour. Each worker produces 5 outputs per hour. How many workers should the firm hour to maximize its profit? What wage will it pay? How much will it charge for each output? What is the profit level of the firm?

3.Suppose the wage rate is \$40 per hour and the rental rate of each unit of capital is \$20. The price of output is constant at 80\$ per unit. Initial capital level is 25. The production function is

– f(E,K) = E1/2K1/2

a) How much labor should the firm employ in the short run?

b) How much labor should the firm employ in the long run?

c) Repeat part (a) when the wage rate is \$10

d) Repeat part (b) when the wage rate is \$10

e) Find the elasticities of short run and long run labor demand curves.

f) according to the theory, which one should have a higher elasticity in absolute terms, short run or long run labor demand curve? Is you finding in part e) consistent with the theory?

Now assume production function is

– f(E,K) = E1/3K1/5

g) if you repeat part(b) with this new production function, for optimal E AND K, we/r k = ? (do not need to solve for optimal E and K.)

Now assume production function is

f(E,K) = E1/3K2/3

h) if you repeat a) and b) with this new production function, can you find the solution? You do not need to solve, just state if it is solvable or not and why?