Solow growth model

Econ 303: HW 2

1. Suppose a household's preferences were represented by the utility function and they faced the following budget constraint: .

Your own personal homework is to use the Lagrangian and solve for the demand functions for x and y. You will be expected to be able to do this fully on an exam, so make sure you can do so. For this assignment though, once you have solved for those, if you were given the values of and , what would the demand for y be?

2. Suppose a household's preferences were represented by the utility function and they faced the following budget constraint: .We discussed constraints and when they are/aren't binding. You have three constraints for this problem:

The budget constraint and two non-negativity constraints (meaning the household is not allowed to purchase negative units of any good) for goods x and y (. For the constraints, your Lagrangian would have a Lagrangian multiplier on each constraint (we typically leave off the ones for x and y when we write the Lagrangian), so we will call the constraints ,, each named for the associated constraint. Given these three constraints, how many constraints would be binding (i.e. how many of the Lagrangian multipliers would have non-zero values?

3. Given the standard Solow growth model with no exogenous growth (simply, the first Solow model version we covered), make sure you can solve by hand (showing all steps) the steady state level of capital per capita, starting with the aggregate path for capital. For this problem, what is the steady state level of capital per capita, given the following variables:

4. Given the standard Solow growth model with no exogenous growth (simply, the first Solow model version we covered), make sure you can solve by hand (showing all steps) the steady state level of capital per capita, starting with the aggregate path for capital. For this problem, what is the steady state level of consumption per capita, given the following variables:

5. Given the standard Solow growth model with no exogenous growth (simply, the first Solow model version we covered), make sure you can solve by hand (showing all steps) the steady state level of capital per capita, starting with the aggregate path for capital. For this problem, given the following variables: ,which economy would have a higher steady state level of consumption, if it has a savings rate of s=0.25 or of s=0.95?

6. Given any Solow economy that has converged to steady state, suppose in period t=10 that there is a new tax policy that offers a tax credit for every child and the population growth rate increases from to . What will be true of compared to ? (greater than, less than, equal to)

7. Given any Solow economy that has converged to steady state, suppose in period t=10 that there is a new tax policy that offers a tax credit for every child and the population growth rate increases from to . What will be true of compared to ?(greater than, less than, equal to)

8. Take the aggregate path for capital and solve for the steady state level of capital per capita in the Solow model. Do not skip any steps. Upload a pdf of the file when you are done. Genius scan is a free app you may wish to use if you do not have access to a scanner.