A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that t

A large share of the world supply of diamonds comes from...

Key Concepts

Cartel Formation

A cartel is an association of independent firms or producers that agree to coordinate their production or pricing decisions in order to exert collective market power. This collusion allows member firms to act like a monopoly by restricting output to raise the market price and increase their joint profits. However, the effectiveness of a cartel depends on the ability of its members to maintain the agreed-upon production quotas.

Incentives to Deviate in Cartels

Within a cartel, individual members may have a strong incentive to cheat on the agreement because by secretly increasing their output, a member can capture additional market share and boost its own profits without bearing the full cost of lowering the market price. This temptation undermines the stability of cartel agreements, often leading to a breakdown of the collusion over time.

Perfect Competition

This concept refers to a market structure in which there are many sellers, none of whom has any significant market power. In such a market, firms are price takers, meaning that the price is determined solely by market demand and supply, generally equating to the point where price equals marginal cost. This results in an efficient allocation of resources and maximizes consumer and producer surplus.

Monopoly

Monopoly describes a market situation where a single firm becomes the sole provider of a certain good or service with no close substitutes. In a monopolistic market, the firm has significant control over the price and output level. The monopolist maximizes profit by setting marginal revenue equal to marginal cost, often resulting in higher prices and lower quantities compared to more competitive markets.

Marginal Cost and Demand Analysis

Marginal cost is the additional cost incurred from producing one more unit of a good, while the demand analysis involves understanding how consumers value additional units at various price points. The intersection of the supply curve, which is often influenced by marginal cost considerations, and the demand curve determines the market equilibrium price and quantity. This fundamental analysis is crucial for understanding different market structures and pricing strategies.

Transcript

00:01 In this example, we're working with the idea of cartels, and we're given the information that russia and south africa both produce much of the world's diamonds.

00:08 And we are given that they have a constant marginal cost equal to $1 ,000.

00:13 And we're also given in the book their demand schedule.

00:16 So it's this big table with the prices and quantities that are associated with one another.

00:19 What i like to do, however, is treat those prices and quantities as coordinate points, and i like to produce a linear function to describe them.

00:27 I think it's much easier to work with less cumbersome than repeatedly having to reference back to this big table.

00:33 So i've found for us that we have quantity equal to 13 ,000 minus p.

00:38 And then solving for p, we have that the price is equal to 13 ,000 minus q.

00:41 And i did that just by solving for a basic linear function, basic algebra that many of us should know.

00:47 So we're going to start by assuming we're working with perfect competition.

00:51 We want to know the price and quantity if there are many sellers in the market, which means the perfect competition, profit maximizing, condition is price is equal to marginal cost.

01:01 And luckily, we were given all of this information already.

01:04 You see, we have this price function of 13 ,000 minus q, setting that equal to our marginal cost of $1 ,000 that was given to us.

01:14 We're able to solve for q is equal to $12 ,000.

01:19 It's fairly straightforward.

01:21 And now if we wanted to find the price, all we need to do is plug this quantity back into our price function, which is equal to 13 ,000 minus q, plugging in 12 ,000 for our quantity, we get a price which is equal to $1 ,000.

01:36 And that would be our price and quantity under perfect competition or in a market where we have many sellers.

01:42 Now let's consider we're working with a monopoly.

01:44 We have only one seller.

01:46 And the only thing that's really changing is this profit maximizing condition.

01:49 And the profit maximizing condition for monopoly is that marginal revenue is equal to marginal cost.

01:55 So working under this, what we already know is that marginal cost is staying constant at 1 ,000, but we need to find marginal revenue.

02:03 And to find marginal revenue, what we first need to do is find total revenue.

02:07 And we know that total revenue is equal to price times quantity.

02:12 Well, we were given this price function where 13 ,000 minus q is equal to our price.

02:18 We're just going to plug that in for this price value, 13 ,000 minus q.

02:23 And we're just going to multiply that by another q.

02:27 Simplifying this, we get a total revenue, which is equal to 13 ,000 q minus q squared.

02:36 And then to find our marginal revenue, we just need to take the derivative of total revenue with respect to q, which gives us 13 ,000 minus 2q for marginal revenue.

02:47 And then let's just go ahead and set that equal to this marginal cost that we said is equal to 1 ,000 so that we can solve for that profit maximizing conditions.

02:56 So setting that equal to our marginal cost of 1 ,000, what we can now do is solve for q.

03:01 And solving for q here, what we're able to find is that q is equal to 6 ,000.

03:08 So under monopoly, we have a quantity equal to 6 ,000.

03:12 And then price is again pretty straightforward.

03:14 We're just going to plug it back into our price function, which is 13 ,000 minus q.

03:19 Plugging in that 6 ,000, it gives us a price, which is equal to $7 ,000.

03:28 All right.

03:28 Now let's assume russia and south africa form a cartel together to sell these diamonds.

03:35 So under a cartel, they're still working with this profit maximizing condition that they were under monopoly, where marginal revenue is equal to marginal costs.

03:41 So we can know that under this cartel, we still have a price which is equal to $7 ,000 and a quantity which is equal to $6 ,000.

03:54 That hasn't changed.

03:55 However, the profits in this case are going to be split evenly amongst the two countries.

04:00 So let's go ahead and figure out what our total revenue would be here.

04:04 And total revenue being equal to price times quantity is going to be our price of $7 ,000 times our quantity of $6 ,000, which gives us a total revenue that's equal to $42 million.

04:21 But we want to know the profits.

04:23 And what we know of profits is that profit is equal to total revenue minus total cost.

04:32 So we just found our total revenue.

04:34 Which is 42 million.

04:36 And total cost we can calculate as 1 ,000, which is our marginal cost times q.

04:45 And q in this case we said is 6 ,000...

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