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Suppose that the desired capital stock is given as:
K* = 0.3Y/ir
Where Y = GDP, and ir is the real interest rate. Suppose further that Y = $5 trillion and that
ir = 0.12 (12 percent).
a. Calculate the desired capital stock, K*.
b. Now suppose that Y rises to $6 trillion. What is the corresponding (or new) desired capital stock?
c. Suppose that the actual capital stock (K) was equal to the desired capital stock (K*) before the increase in income from $5 trillion to $6 trillion. Assume that a gradual adjustment process of actual to desired capital occurs, such that λ = 0.4. What will the level of investment be in the first year after the change in income? What will investment be in the second year after the change in income?
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