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Question

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Economi and workers. The aggregate produc sented by the following production function: Y AK L-. Workers earn an income that is used for both consumption and investment. Investment increases the mimber of machines from year to year following this capital accumulation equation : Kt+1 =(1-5)Kt+sy, Given these two equations, the equilibrium number of machines is given by K* = L × ( Using these three equations, answer the following questions. nction of goods and services requires technology, machines tion that describes this process can be repre- I. Both the US and Canada have one million workers who consume 90% of their income. The depreciation rate in machines is 10% in both countries and technological progress is equal to 1, The US places a high value on machines (35%) while Canada places a high value on workers (75%). Calculate the number of machines in equilibrium for the US and Canada. Which of the two countries has a higher number of machines in equilibrium? Why?

Explanation / Answer

See here we have given a problem regarding economic growth, here we also given the equilibrium value of “K” also in parametric form. Now in “US” and in “Canada” the values of the parameters are not same, and according we need to find out the numeric equilibrium value of "K" given the parametric information regarding the 2 country.

So, the equilibrium value of “K”, is “L*[sA/d]^(1/1-a).

In “US and Canada”, L=1million, consume 90% of their income, => s=10%=0.1, d=10%=0.1 and “technological progress=1”, A=1.

But, US places higher value on machines ”35%”, => for US a=35%=0.35, on the other hand Canada places higher value on “L”, => 75%, (1-a)=0.75, => a=0.25.

So, now we can calculate the final equilibrium value of “K” for both countries.

So, for both of them the equilibrium value of “K” is same.

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