Question - In this question, I will guide you through a simple AK model. The so-called AK model is a special case of the Solow Model. The production function is simply Y = AK so 1/3 for capital in the last question becomes 1, 2/3 for labor becomes 0 (L0 = 1). We add an A to denote technology. The special feature of the AK model will help you understand the Solow model better!
a. Does the production function have increasing returns to scale?
b. Does the production function have diminishing marginal returns to capital?
c. What's is the per capita production function, y = f(k)?
d. Assume there is no population growth or technological progress. Capital depreciation rate delta = 20%, saving rate s = 10%. Write the law of motion for k.
e. For what value of A will this economy keep growing and hence no steady state?
f. What's the intuition behind the non-stopping economic growth in this model?