Assume that a country's production function is =^1/3^1/3.

a. Suppose that the country has 729 units of labor and 4,096 units of capital. What is the value of ? What is the value of per-worker capital stock, (to two decimal places)?

b. Derive the per worker production function =()? Graphically illustrate it.

c. Suppose that the savings rate is 20%. Also assume that the economy is currently at a steady state level of per worker capital stock (in other words, the you found in part (a) is the steady state ). What is the depreciation rate (as a percentage to one decimal place)?

d. Given the values associated with equilibrium that you found in part (c), what is consumption per worker in this economy in steady state? Graphically illustrate it. e. Calculate the golden rule level of capital gold for this economy. Is the steady state capital-labor ratio of the economy above or below that of the golden rule? Graphically illustrate. Is the steady state level of consumption above or below the golden rule level of consumption?