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Question: 2 there are two industries hatching and laying and two...

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2. There are two industries, hatching and laying, and two goods, eggs and chick- ens. The price of an egg is l; the price of a chicken is p. The hatching industry produces y chickens using x eggs, which it buys from the laying industry. Its production function is yi-4(x1)2. The laying industry produces x2 eggs using chickens, which it buys from the hatching industry. Its production function is x,-(y2)1/2. (We assume away any consideration of time lags, non negativity constraints, the indivisibility of live chickens or eggs, and claims to precedence by all parties.) Express in terms of p the profit-maximizing quantities of chickens and eggs produced or used in each industry. Assuming that all eggs produced in the laying industry are used as inputs by the hatching industry, what is the value h the net output p fhc indus of p? What, then, is the net output of chickens available for consumption?

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