5. The demand function of a company is Q-20-0.4p. (1) Please derive its inverse demand function,...

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5. The demand function of a company is Q-20-0.4p. (1) Please derive its inverse demand function, i.e., express p as a function of Q. (Q stands for quantity demanded, and p is the market price). (2) What is the marginal revenue function? 2 (3) If the marginal cost of the company is $10. What is the optimal quantity that maximizes its profit? What is the maximized profit? (4) Graph the marginal cost and marginal revenue function in (Q, p) space. Indicate their intercepts on each axis. Indicate the optimal output and price in the graph. (5) Suppose the marginal cost decreases to $8. What is the optimal quantity? Does it increase, decrease, or stay the same? In the same diagram from (5), graph the change of marginal cost function, optimal quantity, and optimal price (if there is any change at all). 6. Suppose that you can sell as much of a product as you like at $92 per unit. Your marginal cost (MC) for producing the Qth unit is given by: MC-10Q. If fixed costs are $350, what is the optimal output level? 7. Suppose a firm has as its total cost function: TC = 24 + 202, and its output can be sold at $44 per unit. Using calculus to find the firm's profit-maximizing output. What is the maximized profit? 5. The demand function of a company is Q-20-0.4p. (1) Please derive its inverse demand function, i.e., express p as a function of Q. (Q stands for quantity demanded, and p is the market price). (2) What is the marginal revenue function? 2 (3) If the marginal cost of the company is $10. What is the optimal quantity that maximizes its profit? What is the maximized profit? (4) Graph the marginal cost and marginal revenue function in (Q, p) space. Indicate their intercepts on each axis. Indicate the optimal output and price in the graph. (5) Suppose the marginal cost decreases to $8. What is the optimal quantity? Does it increase, decrease, or stay the same? In the same diagram from (5), graph the change of marginal cost function, optimal quantity, and optimal price (if there is any change at all). 6. Suppose that you can sell as much of a product as you like at $92 per unit. Your marginal cost (MC) for producing the Qth unit is given by: MC-10Q. If fixed costs are $350, what is the optimal output level? 7. Suppose a firm has as its total cost function: TC = 24 + 202, and its output can be sold at $44 per unit. Using calculus to find the firm's profit-maximizing output. What is the maximized profit?

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1 To derive the inverse demand function we can solve the demand function for p in terms of Q Given Q 20 04p Rearranging the equation to solve for p 04p 20 Q p 20 Q 04 p 50 25Q Therefore the inverse de... View the full answer