In the Solow Growth Model, explain how consumption level changes in the long run when consumption is decreased in the short run.
In the Solow Growth Model, there are 5 key equations to know in order to solve the model. Production function: Yt = AKt1/3Lt2/3Capital accumulation: ΔKt+1 = It - dKtLabour supply: Lt = L Resource Constraint: Ct + It = Yt Allocation of resources: It = sYtIn the SGM, there are only two options for output as shown by the resource allocation (4) - consumption or investment. In this way, it is a closed system. Therefore if we reduce consumption, for that equation to balance, investment will have to increase. Now we need to consider what happens if investment increases. If we look at the capital accumulation equation (2), if I increases, then ΔKt+1 will increase because nothing about the depreciation curve has changed. As it doesn't have a t subscript, delta is a constant (tends to be estimated at 10%). As the the capital accumulation increases, so does the capital stock. Now from the production function (1), we can see that an increase in K leads to an overall increase in output as well. As output increases, the resource constraint shows that both investment and consumption increases also. Therefore, the answer to the question is, that if we decrease consumption in the SR, in the LR it leads to an increase in consumption as the extra investment gets converted to capital accumulation which increases overall output. While the proportion of the output that goes to consumption might be less, absolute level of consumption increases.
