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Expressions for the demand function

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Suppose we have the following expressions for the demand function, marginal revenue (MR), total cost (TC) and marginal cost (MC) where P is price and Q is quantity:

Demand:

Marginal Revenue:

Total Cost:

Marginal Cost:

P = 2600 - 20Q or Q = 130 - 0.05P MR = 2600 - 40Q

TC = 80 + 1000Q + 20Q2

MC = 1000 + 40Q

From this, we know that the derivative of quantity demand with respect to price

(or dQ/dP) equals -0.05.

a. At what value of price and quantity is the price elasticity of demand (or ?p) equal to -1? What is the total revenue at this point? Is there anything special about that total revenue (referring to the week 1 problem might help)?

b. Suppose Q = 40. What is the value of the price elasticity of demand, ?p?

c. Suppose that in a different market with an unknown demand curve, we know the price elasticity of demand (?p) equals -5. If the marginal cost equals $400, what is the value of the optimal price?

Reference no: EM133130113

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