Consider an economy with two goods $(1$ and $2),$ H consumers and m

firms. Consumer have preferences modelled by the utility

$=1$

$2$

$,=1,...,$

and a share $$

$=1/$ in firms $=1,...,.$ All consumers are endowed

with two units of good $1$ and $0$ units of good $2.$ Each firm has a

technology characterized by the following production function:

$2$

$=[2$

$$

$]$

$1/2$

$,=1,...,.$

a$.$ Calculate the profit maximizing choices of the firms, consumer

demand for each good and the competitive equilibrium

b$.$ Explain what happens to prices when $($i$)$ increases, $($ii$)$

increases and $($iii$)$ offer an explanation for why this happens.

c$.$ Suppose that for all consumers the endowment of good $1$ increases

from $2$ to $2(1+),$ explain the impact on prices.

d$.$ What is the effect of changing the distribution of endowments

among consumers?