Consider an economy with two goods $(1$ and $2),$ H consumers and m firms. Consumer have preferences modelled by the utility Uh $=$ x$1$ hx$2$ h$,$ h $=1,...,$ H and a share $\backslash$theta j h $=1/$H in firms j $=1,...,$ m$.$ 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: y$2$ j $=[$y$2$ j $]1/2,$ j $=1,...,$ m$.$ 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$)$ H increases, $($ii$)$ m 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 $2(1+\backslash$delta $),$ explain the impact on prices. d$.$ What is the effect of changing the distribution of endowments among consumers?