Compensate the firm for the additional cost

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A firm uses gas (g) and machinery (m) to produce yachts(y), according to y=g0.5m0.5 .The firm chooses to produce 100 yachts, because there is exactly that much demand. The price of gas is 10, and the price of machinery is 20.

The marginal product of gas is 0.5(m0.5/g0.5) and the marginal product of machinery is 0.5(g0.5/m0.5)

How do I calculate the cost minimizing choices of g and m?

Then if the government raises the price of gas to 30 through a carbon tax and offers the firm compensation to exactly compensate the firm for the additional cost, how do I calculate how much they are going to compensate them exactly?

Reference no: EM132163700

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