Answer to Question #283979 in Macroeconomics for diliz

Question

Consider a Solow growth model with the following production function:

 (1) If A = 2, L = 20,000, and K = 400, what is output?

 

 (2) Does this production function have constant returns to scale? Explain.

 

 (3) Suppose the labor force grows by 5% so that it is now 21,000. By how  

    much does output increase?

 

 (4) Starting again with the conditions in part (1), what if capital increases by

    5%, so that it is now 420. By how much does output increase?

 

Answer 1

1) K^0.3(AL)^0.7= Y

What is the output if A = 2, L = 20,000, and K = 400?

Y = 10,047.5 Y = 10,047.5 Y = 10,047.5

2) Since the proportional increase in all inputs is equal to the proportional increase in output (production), returns to scale are constant.

3)Let's say the labor force increases by 5% to 21,000 people. What is the increase in output?

The total output will now be 10,396.6, up 3.5 percent.

4) Starting with the conditions in part a, the capital increases by 5%, making it 420. What is the increase in output?

The output will now be 10,195.7, a 1.5 percent increase.