: 0.4 0.4 An economy has at its disposal two possible technologies Y₁ = 2KA ; Ув = 6kB Where y is output per worker and k is capital per worker. Access to technology A has no cost, while using technology B implies paying 20 at once and for all. Assume the saving rate is 0.25, labor grows at 0.02, and capital depreciates at 0.03. Answer the following: a) At what level of capital per worker should you pay to have access to technology B? b) Calculate the capital, product and consumption per worker of the stationary equilibrium if you use technology A, what are their values if you use technology B c) If the initial capital per worker is 5, what will be the stationary equilibrium of this economy? What if the starting capital was 70.

A. The level of capital per worker at which you should pay to have access to technology B depends on when the marginal product of capital for technology B exceeds the marginal product of capital for technology A.

To determine the level of capital per worker at which you should pay for access to technology B, we compare the marginal product of capital (MPK) for technology B with that of technology A. The MPK represents the additional output produced by an additional unit of capital.

For technology A, the MPK is 2A, and for technology B, the MPK is 6B. To find the level of capital per worker at which you should pay for technology B, we set up the following inequality:

6B > 2A

Simplifying, we get:

3B > A

Next, we consider the steady-state equilibrium of the economy. In the steady state, investment (determined by the saving rate and output) equals depreciation (determined by the depreciation rate and capital). By setting up this equation, we can calculate the steady-state level of capital per worker (k*) using the following formula:

k* = (0.5A) / 0.03

With technology A, the steady-state capital per worker (k*), output per worker (y*), and consumption per worker (c*) can be calculated as follows:

k* = (0.5A) / 0.03

y* = 2A

c* = y* - (0.25y* - 0.03k*)

To analyze the equilibrium with technology B, we need to determine the capital per worker threshold at which it becomes beneficial to switch to technology B. This threshold occurs when the MPK for technology B exceeds that of technology A, which is represented by the inequality:

6B > 2A

Once this condition is met, we consider the steady-state equilibrium with technology B, where the capital per worker (k*), output per worker (y*), and consumption per worker (c*) can be calculated in a similar manner as with technology A.

For the given question, the specific details regarding the saving rate, labor growth rate, and depreciation rate are not provided. Additionally, the initial capital per worker values of 5 and 70 are mentioned without further context. Therefore, to provide a precise answer, the missing information would need to be specified.

In summary, the determination of the capital per worker threshold for accessing technology B, along with the calculations of the steady-state equilibrium for both technologies A and B, allows us to understand the effects of different technologies on the economy's capital, output, and consumption per worker.

Learn more about Technology

brainly.com/question/15059972

#SPJ11.