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Tutorial 10: Firms With Market Power (cont.)

 

The Monopolist's Output Decision

A firm's goal is to maximize economic profit. As we learned in Tutorial 9, economic profit is at its highest when the marginal cost of the last unit produced equals the marginal revenue of the last unit sold. That is, given

P(Q) = R(Q) - C(Q)
P(Q) is maximized when MR(Q*) - MC(Q*) = 0.

(Do you want to review why?)

 

In Figure 3, the profit-maximizing level of output for this price-setting firm is shown at Q* = 3000 units/t, where MR1 = MC1. Remember that this price-setting firm does not take the market price as given. Thus, after it sets a target level of output, it must decide what price to charge. Recall from Tutorial 2 that market demand shows the maximum willingness to pay for a given quantity. That means the firm should look to the demand line at its desired level of output to see the maximum price that someone will pay for that last unit. Draw a vertical line up from the x-axis at Q* = 3000 units/t until the line hits the demand curve. Then continue that line horizontally to the left until it reaches the vertical axis. That marks the highest price, P* = $70 per unit, the firm can charge and still sell the last of the 3000 units. For all previous units, some buyers are willing to pay more, but this firm sets just one price for all the units it sells.

 

Figure 3


Graph showing D and MR for a price setting firm, with MC and ATC added to show how Q-star and P-star are determined.

 

We know this output and price will generate the highest economic profit possible for the firm, but how high is it? Just because economic profit is at a maximum does not mean it is large -- or even positive!

In Tutorial 9b we learned that total profit can be calculated as the difference between price and average cost times the level of output sold. Graphically, we can find the ATC(Q*) by drawing a vertical line up from the profit-maximizing output level, Q*, until it reaches the ATC curve. Then continue that line horizontally to the left until it reaches the vertical axis. The point at which that line hits the vertical axis tells us the average total cost of producing all Q* units per period. The rectangle (P* - ATC*) · Q* shows the size of the economic profit earned by this firm from the sale of Q* units of output at a market price of P*. According to the Excel workbook for this Tutorial, that economic profit amounts to just over $55,000.

 

Example [from MonopQ.xls] Top of page.

Before turning our attention to the Excel workbook accompanying this Tutorial, let's work through a numerical example.

Let total cost be written as C(Q) = 75000 + 10·Q + 0.005·Q
FC = 75000, VC = 10·Q + 0.005·Q
AC = 75000/Q + 10 + 0.005·Q
MC = 10 + 0.01·Q

Let inverse demand be written as P(Q) = 100 - 0.1·Q
TR = 100·Q - 0.1·Q2
MR = 100 - 0.2·Q  

Plot just the marginal product curve. [Plotting cells in nonadjacent columns.]

Remember the steps a profit-maximizing firm must follow when deciding output and price?

Step 1: To maximize P, set Q* such that set MR - MC = 0:

(100 - 0.2·Q) - (10 + 0.01·Q) = 0
90 = 0.03·Q
Q* = 3,000 units/t.

 

Step 2: Set the highest price buyers are willing to pay:

From inverse demand, P* = $70 per unit.

 

Step 3: Calculate P:

P(Q*) = (P* - AC*)Q*
where AC* = 75000/3000 + 10 + 0.005 · 3,000
= (70 - 50) · 3,000
P(Q*) = $60,000.

 

Step 4: Because economic profit is positive, Step 4 does not apply...

 

A Rule of Thumb for Pricing Top of page.

Many economics students find all this talk of how a price-setting firm chooses price and output to be a bit removed from the reality of decision making by a real firm. While there is no doubt that firm's often price just to get close to as high a profit as possible, there is a relatively simple way to apply these concepts to finding the P-max price and output in the real world.

            • Recall that MR = P + P·One over E sub p..

            • Then, note that MR = MC at P max, so P + P·One over E sub p. = MC.

                  Rearranging terms, we get The difference P minus MC over P. = -One over E sub p.

                  This gives us a rule of thumb for pricing:

                                   The difference P minus MC over P. is the markup over marginal cost as a % of P,

                                    which says that the markup should equal to -One over E sub p..

If we rearrange the equation we can write P as a function of MC and Ed:

                                    P =  MC divided by the sum of 1 plus 1 over E sub p.    ...if Ep = -2.33 and MC = $40,

                                                            then P = 40 divided by the sum of 1 plus one over -2 and one third.= 40 divided by 0.571429 = $70 / unit.

This is approximately a 43% markup over marginal cost (at the firm's P-maximizing level of output).

This result of all this mathemagics tells the firm that the size of the markup they may set (as a percent of price) depends on price elasticity of demand for their product. That is, the more responsive buyers are to an increase in price (i.e., the more price elastic demand is), the smaller the markup. But the less responsive they are to a price increase, the larger the markup possible. Why?

Recall from Tutorial 4 that one of the four determinants of buyer responsiveness is the availability of close substitutes. Thus, demand that is price elastic can indicate the availability of many substitutes for this firm's product. So raising the price just chases the firm's customers to a firm producing a similar product. When demand is price inelastic, raising the price may leave customers grumbling, but with few, or no, substitutes available they have few, if any, choices...

 

Now it's time to "do the thing".

Click on the following link to download the Price-setting Firm Workbook. Work through Question 1. This will let you practice with the model of how a price-setting firm chooses the profit-maximizing level of output and sets the price for the product. 

Return here when you have finished.

Need help downloading the Excel file?

 

This is a good time to start, or review, GFE 22, question 1.

 

In this part of Tutorial 10 we have discovered that even firm's with market power, able to set their own product price, must set output such that MR - MC = 0 in order to maximize profit. They can then set a price for that output (rather than have the market set it for them), but that price cannot be higher than the maximum willingness to pay of the buyer who purchases the last unit of the firm's output. So we can discard one street myth about firm's with market power -- that they can set any price they please! The law of demand constrains their greed regardless the magnitude of their market power

In part c of this Tutorial we will look more closely at the sources of a firm's market power as well as the limitations of that market power in the long run.