11. (30, 2);A. (15 POINTS) Use calculus to prove that marginal revenue is positive when a good is inelastic and vice versa.;B. (10 POINTS)Use calculus to prove that for an inelastic good when price increases total revenue also increases, but when the good is elastic total revenue falls with an increase in price.;C. (25 POINTS) Use Calculus to derive the quantity that a company should sell in order to maximize profits. Be sure to include any second order conditions necessary to ensure that profit is maximized rather than minimized. Finally draw a graph of total revenue, total costs and profits demonstrating the proper profit maximizing quantity.;12. (15,1) Prove that in an n-commodity world, the marginal rate of commodity substitution (MRCS) between any two commodities, both of which are consumed, must be exactly equal to the price ratio.
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