of stocks negotiated at each $t.$ Show that in equilibrium the total market value

of the firm, $V_t,$ equals the market value of physical capital installed at the end of

each period, $K_{t+1}.$

$($d$)$ Assume now that the firm negotiates a risk$-$free bond with the household. Hence,

dividends distributed to stockholders are now given by:

$d_t=Y_t-I_t-{}_t+B_{t+1}-R_t{B}_t.$

Show that in equilibrium the following must be satisfied: $V_t+B_{t+1}=K_{t+1}.$ Is

this result connected with the Modigliani$-$Miller Theorem? ${?}^2$

$($e$)$ Discuss how the total market value of the firm, $V_t,$ may differ from the market

value of physical capital installed at the end of each period, $K_{t+1},$ in the presence

of a tax on dividends ${}_d.$

$($f$)$ Given your results in the previous question, explain Figure $(2)$ below.