# Lecture notes week 8

ECMA04H â€“ Week Eight

The Monopoly Model

a. The monopoly model. How does monopolist behave? What are the results?

b. Inefficiency and monopoly. Dynamic efficiency vs. allocative efficiency.

c. Where does monopoly come from; what conditions are necessary; what are the public policy responses?

d. Excise tax on a monopoly

i Only one supplier. Entry to market is blocked.

i Single seller faces entire market demand curve (price maker, not price taker)

What about Marginal Revenue (MR)?

MR = dTR / dq or dTR / dQ

TR = P x Q. To PC firm, P was a constant (price taker)

To monopolist, P is a choice variable, so we must treat P as a function of Q

So, MR = [(dP / dQ) x Q] + [(dQ / dQ) x P] or MR = P + Q (dP / dQ)

For a linear demand curve P = a â€“ b Q,

MR = (a â€“ b Q) + (Q [-b]) = a â€“ 2 b Q

So MR has the same intercept and twice the slope of the linear demand curve

Algebraic example of monopoly industry

Market Demand: P = 100 - .02Q

So, total revenue = TR = P x Q = 100Q - .02Q2

Marginal Revenue = dTR / dQ = 100 - .04Q (the rate at which total revenue is changing as output increases)

Assume total cost function of monopoly firm is:

TC = .01q2 + 10q + 432 or .01Q2 + 10Q + 432

So, MC = .02Q + 10 (the rate at which total cost is changing as output increases)

AC = .01Q + 10 + 432Q-1

We can solve by forming the profit function and maximizing with respect to Q

3 = TR â€“ TC = (100Q - .02Q2) â€“ (.01Q2 + 10Q + 432) = 90Q - .03Q2 â€“ 432

Therefore, d3/dQ = 90 - .06Q

Setting = 0, we have .06Q = 90 or Q* = 1500

Substituting into the demand function, we have P* = 100 - .02(1500)= $70

Alternative (easier) solution method

We can set MC = MR and solve for Q

MC = .02Q + 10

MR = 100 - .04Q

.02Q + 10 = 100 - .04Q or .06Q = 90 or Q* = 1500

Substituting into the demand function, we have P* = 100 - .02(1500)= $70

How much is the profit of the monopolist?

Profit = TR â€“ TC = (70 x 1500) â€“ (0.01 x 1500 x 1500 + 10 x 1500 + 432) = $105000 - $37932 = $67068

Where is the monopolistâ€™s supply curve?

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## Document Summary

What are the results: where does monopoly come from; what conditions are necessary; what are the public policy responses, excise tax on a monopoly. E single seller faces entire market demand curve (price maker, not price taker) To pc firm, p was a constant (price taker) To monopolist, p is a choice variable, so we must treat p as a function of q. So, mr = [(dp / dq) x q] + [(dq / dq) x p] or mr = p + q (dp / dq) For a linear demand curve p = a b q, Mr = (a b q) + (q [-b]) = a 2 b q. So mr has the same intercept and twice the slope of the linear demand curve. So, total revenue = tr = p x q = 100q - . 02q2. Marginal revenue = dtr / dq = 100 - . 04q (the rate at which total revenue is changing as output increases)