A firm chooses its desired future capital stock, K^f . Initially, the firm chooses K_0^f . Then the firm learns that the depreciation rate, \delta, will increase and that future Total Factor Productivity, A^f , will also increase. The interest rate is positive and remains unchanged, and the price of investment goods is constant over time: p_k=p_k^f . Buying one additional unit of capital costs p_k units of output and takes place one period before the capital is used in production. In the following period, the additional unit of capital increases output by MPK^f . After production, the undepreciated part of the capital can be sold at a price p_k^f per unit.
This is the same timing and investment problem studied in class; no change in the setup is intended. Which of the following statements is correct?

Question

A firm chooses its desired future capital stock,   K^f . Initially, the firm chooses   K_0^f . Then the firm learns that the depreciation rate,   \delta,  will increase and that future Total Factor Productivity,    A^f  , will also increase. The interest rate is positive and remains unchanged, and the price of investment goods is constant over time:   p_k=p_k^f .   Buying one additional unit of capital costs   p_k  units of output and takes place one period before the capital is used in production. In the following period, the additional unit of capital increases output by   MPK^f . After production, the undepreciated part of the capital can be sold at a price   p_k^f ​ per unit. 
 This is the same timing and investment problem studied in class; no change in the setup is intended. Which of the following statements is correct?

Answer

If the percentage increase in   A^f  and the percentage increase in   \delta  are the same,   K^f  will be larger than    K_0^f

Answer

K^f  will be larger than    K_0^f

Answer

If the percentage increase in   A^f  and the percentage increase in   \delta  are the same,   K^f  may be either larger or smaller than    K_0^f

Answer

K^f  will be smaller than    K_0^f

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A firm chooses its desired future capital stock, K^f . Initially, the firm cho...

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