microfoundations: investment

Question 1

what are the two reasons for the stock of fixed capital to change?

Answer 1

gross investment adds new building and machines
depreciation at a rate δ reduces the available capital : machines break down or become obsolete, buildings have to be torn down or repaired

Question 2

what is the optimal capital stock?

Answer 2

the level of capital accumulation that achieves profit maximisation of a representative firm

Question 3

what is the representative firms production function in period t?

Answer 3

Y_t= A_t * F(L) where F’>0 and F’‘<0

Question 4

what is the representative firms production function in period t+1?

Answer 4

Y_t+1 = A_t+1 * F(K) where F’>0 and F’‘<0

Question 5

what is the general dynamics of fixed capital?

Answer 5

K_t+1= K_t - δK_t + I_t <=> K_t+1 - K_t = I_t -δK_t where we assume K_t=0 as capital only appears in the second period as a result of investment made in the first period

Question 6

what is the equation for the firms profit in the period t?

Answer 6

Π-t= A_t *F(L) -wL-I_t

Question 7

what is the equation of the firms profit in the period t+1?

Answer 7

Π_t+1 =A_t+1 *F(K) + (1-δ)K

Question 8

what is the optimality condition for capital and what does this mean?

Answer 8

A_t+1F’(K) = r +δ
this condition pins down optimal capital stock of the second period K and therefore optimal investment today

Question 9

what is δ +r?

Answer 9

the user cost of capital

Question 10

what is the depreciation cost?

Answer 10

wearing out of capital stock

Question 11

what is the interest rate cost?

Answer 11

cost of funds and the forgone current profit
- firms may have to borrow to buy equipment
if firms use retained earnings, they give up the interest payments that would have received if invested in financial assets instead of buying new equipment

Question 12

if the user cost of capital is greater than the marginal product of capital then what should the firm do?

Answer 12

it is profitable for the firm to reduce the capital stock

Question 13

if the user cost of capital is less than the marginal product of capital then what should the firm do?

Answer 13

it is profitable for the firm to increase the capital stock

Question 14

how do stock prices reflect the incentive to invest?

Answer 14

stock prices tend to be high when firms have many opportunities for profitable investment
these profit opportunities mean higher future income for shareholders

Question 15

what is the stock market value of a firm?

Answer 15

the stock market value of the firm is a discounted value of profits it will earn today and in the future

Question 16

what is the book value of a company?

Answer 16

the book value of a company measures its accumulated investment, net of depreciation ( resale value of the firms capital stock at market prices)

Question 17

why might the market value of the firm deviate from its book value ?

Answer 17

it might deviate due to adjustment costs. expanding a firm involves paying a cost of physically installing new machines, training workers to use them etc

Question 18

what is tobins q formula?

Answer 18

tobins q = market value of firm/ replacement cost of capital

Question 19

if q is greater than 1, what does this mean?

Answer 19

market value is greater than book value. market signals that the value of the firm is greater than its capital so firm should invest more capital

Question 20

if q is equal to 1, what does this mean?

Answer 20

zero investment, installed capital has the same value as the market value

Question 21

if q is less than 1, what does this mean?

Answer 21

value of the firm is less than the value of the capital, firm should disinvest, the owners are better of selling installed capital

Question 22

what would occur to a firm that develops a new product that raises its future productivity with no adjustment costs?

Answer 22

the firm should expand immediately
this expansion will reduce profitability due to diminishing returns to capital
this company should expand until the marginal product of capital is equal to the user cost where the market value of the firm is equal to the capital stock

Question 23

what would occur to a firm that develops a new product that raises its future productivity with adjustment costs?

Answer 23

expanision will occur gradually ( large changes in capital are more costly than small gradual changes)
the value of the firm may differ for a while from the value of its capital

Question 24

without adjustment costs, what would investment be when q>1?

Answer 24

the investment will be infinite when q>1 without adjustment costs

Question 25

without adjustment costs what would investment be when q<1?

Answer 25

zero investment when q <1 without adjustment costs

Question 26

what is the correlation between tobins q and investment?

Answer 26

there is a postive correlation and this has become especially strong over the last couple of decades