Climate Change and Economic Growth

Consider an economy in which the level of output in year t (Y_t) is determined by the capital stock (K_t) and the stock of greenhouse gases (GHGs) in the atmosphere (S_t). Population and technology are constant over time. Y_t is measured in dollars of output per person; Kt is measured in dollars per person; and St is measured in tons of GHGs per person. The level of output is given by the equation:

Y_t = 1000K_t^0.25(1-a(S_t/1000)²)(1-b)

In this equation, the parameter a determines the economic costs of climate change the percent reduction in output that occurs when the GHG stock is 1000 tons per person. Damages increase with the square of the GHG stock. The parameter b reflects the costs of environmental policies the percent reduction in output caused by efforts to control GHGs.

10% of output is allocated to capital investment. So the change in the capital stock between years t and t+1 is given by:

K_t+1 = K_t + 0.1Y_t

In the absence of control policies, each unit of output generates 0.002 tons of GHGs, and GHGs are removed from the atmosphere at the rate of 1% per year. So the change in the GHG stock between years t and t+1 is given by the equation:

S _t+1 = 0.002Y_t (1c) + 0.99S_t

In this equation, the parameter c represents the stringency of environmental policies i.e., the percent reduction in GHG emissions per unit of output.

In 2021, the capital stock is K₂₀₂₁ = 10,000 dollars per person, while the GHG stock starts out at S₂₀₂₁ = 500 tons per person.

Question #2 (high damages, no policies)

Now suppose that climate change would be relatively severe so that a GHG stock of 1000 tons per person would reduce output by 10%. In terms of the model, this implies that a = 0.1. In this case, how do output and the GHG stock evolve in the absence of environmental policies (i.e., when b = c = 0)? Add this new model run to the graphs you constructed for Question #1.