Suppose a countrys per capita production function is y=k^05 where y is the per capita water bottle and k is the per capita capital We assume a depreciation rate of 10 01 per year a If the savings rate

In the steady state, the per capita capital (k), per capita output (y), and per capita consumption (c) will be constant over time.

To find the steady state values, we need to find the values of k, y, and c that satisfy the following equations:

Capital accumulation equation: s * y - δ * k = 0
Production function equation: y = k^0.5
Consumption equation: c = (1 - s) * y

Given that the savings rate (s) is 0.4 and the depreciation rate (δ) is 0.1, we can substitute these values into the equations.

Capital accumulation equation: 0.4 * y - 0.1 * k = 0
Production function equation: y = k^0.5
Consumption equation: c = (1 - 0.4) * y = 0.6 * y

Now, we can substitute equation 2 into equations 1 and 3 to solve for k and y:

0.4 * (k^0.5) - 0.1 * k = 0 0.6 * (k^0.5) = c

Solving equation 1 for k: 0.4 * (k^0.5) - 0.1 * k = 0 0.4 * (k^0.5) = 0.1 * k (k^0.5) = (0.1 * k) / 0.4 k^0.5 = 0.25 * k k^0.5 / k = 0.25 k^-0.5 = 0.25 1 / k^0.5 = 0.25 k^0.5 = 1 / 0.25 k^0.5 = 4 k = 4^2 k = 16

Now, we can substitute k = 16 into equation 2 to find y: y = k^0.5 y = 16^0.5 y = 4

Finally, we can substitute y = 4 into equation 3 to find c: c = 0.6 * y c = 0.6 * 4 c = 2.4

Therefore, in the steady state, the per capita capital (k) is 16, the per capita output (y) is 4, and the per capita consumption (c) is 2.4