Discriminating Monopolist's Marginal Revenue
A monopolist charges a uniform price if it sets the same price for every unit of output sold. We discussed this case of pure monopoly in the previous post.
A monopolist price discriminates if it charges more than one price for its output.
Perfect price discrimination occurs when the firm can charge a different price for each consumer, with the price exactly equal to the maximum price the consumer will pay (so called consumer's reservation price). By selling each unit of its output at the reservation price for the consumer buying that unit, the perfectly price-discriminating monopoly's marginal revenue is the same as price.
Therefore, perfectly price-discriminating monopolist has a MR that's identical to the demand curve, and it chooses quantity the same as in the case of pure competition market. And we can see on the graph that price-discriminating monopolist (other things being equal) earns more profit than a normal monopolist does.
Posted by mazoo at 5:14 PM | Comments (1)
May 23, 2005
Pure Monopolist's Marginal Revenue
Market demand is the firm's demand in a case of pure monopoly market structure. Hence, demand curve for a monopoly is downward sloping.
Assume, x - pure monopolist output, P(x) - demand curve formula, therefore P'(x) < 0 (because demand curve is negatively sloped).
TR(x) = P(x) * x - total revenue
Let's differentiate both sides of this equation:
TR'(x) = P(x) + P'(x)*x
MR(x) = P(x) + P'(x)*x, hence
MR(x) < P(x) (because P'(x) < 0,
x > 0)
Where, MR (x) - marginal revenue of pure monopolist.
So, we derived the simple fact that in monopolistic market marginal revenue curve lies below demand curve i.e. marginal revenue is less than price.
Posted by mazoo at 5:24 PM | Comments (2)
February 19, 2005
Substitution and Output effects
Let resources are substitutes and the price of one resource (input 1) has changed. How will demand change for second resource (input 2)?
There is only a resulting table in my Gleim book:
| Price of input1(Price of substitute) | SE v OE | Demand for input2 |
| increase | SE > OE | increase |
| increase | SE < OE | decrease |
| decrease | SE > OE | decrease |
| decrease | SE < OE | increase |
where SE is substitution effect, OE is output effect.
Let's show the given conclusions graphically.
Posted by mazoo at 2:27 PM | Comments (3)
February 18, 2005
MC intersects ATC and AVC at their minimums
Let's consider a simple fact.
Let y - firm's output, TC(y) - total cost, ATC(y)= TC(y)/y - average total cost. Given TC = VC+FC - the sum of fixed and variable cost. And, it must be borne in mind - the short run differs from the long run by the presence of the fixed cost, because all inputs are variable in the long run.
MC(y) = dTC(y)/dy .
The reason that MC intersects ATC and AVC in their minimums is that whatever MC curve below ATC and AVC curves, the latter will decrease (because MC - T additional cost and if MC is less then prior average cost so AC decrease), and vice versa, as long as MC curve exceeds ATC and AVC, the latter will increase.
Formal derivation:
MC(y) = dTC(y)/dy, ATC(y) = TC(y)/y - let's find a minimum point. We equate the derivative to zero.
(ATC(y))' = d(ATC(y))/dy = d(TC(y)/y)/dy = (y* MC(y) - TC(y) )/y^2 = 0
y^2 > 0, hence, y* MC(y) - TC(y) = 0, therefore
MC(y) = ATC(y) in the ATC minimum point (minimum, because in this point (ATC)' < 0 under the condition MC < ATC, and under MC > ATC (ATC)' > 0).
The case with AVC is similar, because d(TC(y)-FC)/dy = MC(y) too.
Posted by mazoo at 6:53 PM | Comments (3)