The Mechanics of Profit Maximization - Essay Example

Marginal Revenue Q = 100 – 0.5P 0.5P = 100 – Q P = (100/0.5) – (Q/0.5) P = 200 – 0.5Q TR = P*Q = (200 - 0.5Q) Q TR = 200Q - 0.5Q^2 MR = dTR/dQ = 200 – Q Marginal Cost TC = 100 + 60 (Q) + (Q) 2 AC = TC/Q = 100/Q + 60 + Q MC = dTC/Dq = 60 + 2Q B) Demonstrate that profit is maximized at the quantity where MR = MC. MR = MC MR = dTR/dQ = 200 – Q MC = dTC/Dq = 60 + 2Q 200 – Q = 60 + 2Q 140 = 3Q Q = 46.67 C) Derive the relationship between marginal revenue and the price elasticity of demand, and show that the profit-maximizing price and quantity will never be the unit-elastic point on the demand curve.

The relationship between marginal revenue and the price elasticity of demand can be summed as the percentage change in revenue equaling total percentage changes in quantity and price. R = PQ dR = PdQ + QdP dR/R = PdQ/PQ + QdP/PQ dR/R =dQ/Q + dP/p D) Using the information in (B), demonstrate that the profit-maximizing price and quantity will never be in the inelastic portion of the demand curve. . 8) Explain the difference between firms in monopolistic competition and firms in oligopoly. What does this difference mean for prices and quantities and for economic profit?

Firms in monopolistic competition contain large number of small firms, while in an oligopoly contain a small number of large firms (Amosweb, 2013). Also, monopolistic firms are price takers, while oligopolistic firms are price setters. Since oligopolies set the prices of quantities rather than take the prices, they can affect the outcome of the economic profit, where if they set the price high, they earn more profit. The monopolistic firms cannot afford to set the prices high because they cannot compete with oligopoly firms in terms of setting prices (Varun, 2013).

With the small number of large firms in oligopoly, it is easier for one firm’s action to influence the action of other firms (Brunelle, 2006). For instance, if one oligopoly firm reduces its price because of increased quantities it will affect the entire market because it would imply other monopolistic firms would have to reduce their prices and may reduce their profit. 9) A firm has estimated the following demand function for it products: Q = 8 – 2P + 0.10I + A Where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month thousands.

Assume that P = $10, I = 100, and A = $20. Based on this information, calculate values for: Quantity Demand Q = 8 – 2P + 0.10I + A Q = 8 – 2 (10) + 0.10(100) + 20 Q = 18 Price Elasticity of Demand ed = dQ/dA ed = 1 Advertising Elasticity ae = dQ/dA x A/Q ae = (1) x (20/18) ae = 1.11 % meaning 1 percent