Consider an economy with three types of investor. There are individuals who are taxed at

high rates on dividend income and low effective rates on capital gains, corporations who

pay a high effective tax rate on capital gains and a low rate on dividend income and

institutions that pay no taxes on dividends or capital gains. There are three types of stock

in this economy, low payout, medium payout and high payout. The before tax and after

tax $($i$.$e$.$ after paying dividends and capital gains taxes at the appropriate rates$)$ total

payoffs per share on these three types of stock for the three groups are as follows.

Stock Low Payout Medium Payout High Payout

Before$-$tax Payoffs $$25$ $$25$ $$25$

After$-$tax Payoffs for

Individuals $$18$ $$16$ $$12$

Corporations $$17$ $$19$ $$21$

Institutions $$25$ $$25$ $$25$

The total amount of low, medium and high payout stock in the economy is $$750$ million,

$$900$ million and $1,400$ million respectively. Individuals' and corporations$$ total holdings

of stock are $$600$ million and $$400$ million respectively. All three groups are risk neutral

and choose the stocks they invest in to maximize their after$-$tax income.

$($a$)$ Give a table showing the equilibrium holdings of individuals, corporations and

institutions of low, medium and high payout stocks respectively.

$($b$)$ If the price of the medium payout stock is $$150$ per share, what are the prices of

the low and high payout stocks, respectively? Explain briefly why they must take

on these values.Consider an economy with three types of investor. There are individuals who are taxed at

high rates on dividend income and low effective rates on capital gains, corporations who

pay a high effective tax rate on capital gains and a low rate on dividend income and

institutions that pay no taxes on dividends or capital gains. There are three types of stock

in this economy, low payout, medium payout and high payout. The before tax and after

tax $($i$.$e$.$ after paying dividends and capital gains taxes at the appropriate rates$)$ total

payoffs per share on these three types of stock for the three groups are as follows.

Stock

Before$-$tax Payoffs

$$25$

$$18$

$$17$

$$25$

Medium Payout

$$25$

High Payout

$$25$

After$-$tax Payoffs for

Individuals

Low Payout