Consider the following model combining the Solow model and the Romer model:

= ¹

₊₁ =

+ =

= bar

a) Assume initially that = 0, ₀ = 1 , bar = 0.02, = 0.00001, = 10,000, the depreciation rate = 0.1 , =0, ₀ = 500,000.

What type of model is that?

Find the growth rate of knowledge in the economy.

Find the growth rate of output per person.

Find the growth rate of consumption per person.

b) Now assume that = 0.3, ₀ = 1 , bar = 0.02, = 0.00001, = 10,000, the depreciation rate = 0.1 , =0.3, 0 = 500,000.

Using Excel or the similar software find the values of , , output per person and consumption per person in periods 1, 5, 10, 20, 50, 100 and 200.

What are the growth rates of these variables from period 0 to period 1, from period 4 to period 5, from period 9 to period 10, from period 19 to period 20, from period 49 to period 50, from period 99 to period 100 and from period 199 to period 200?

Plot output per person from period 0 to period 200 on a graph.