Question

# 1. Consider a basic monopoly model where: The Inverse demand p=P(q) & Cost function is c(y).There...

1. Consider a basic monopoly model where: The Inverse demand p=P(q) & Cost function is c(y).There is a single uniform price to all consumers.Use algebraic expressions to answer all of the following for question 1.

a. What is the monopoly’s problem?

b. Given the cost function and the inverse demand equations set up the first order condition. Solve the first order condition and outline the monopoly’s pricing rule?

c.The total change in revenue that follows an increase in output is given by the MC equation. Use the optimality condition to show the demand elasticity of the monopoly, where |ε(y) | is the demand elasticity.

d. Under monopoly output would not be maximized when MR is negative. Use the elasticity expression to show why. Hint. In a competitive market, the firm faces a horizontal demand curve (i.e. infinitely elastic, |ε(y)|= ∞). Thus the optimality condition is just P= MC.

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