The Krugman Model Let’s describe monopoly first. The demand curve that the firm faces is a straight line: q = α-βp where q = number of units the firm sells p = the price per unit α and b are constants. We can isolate p p 1 q The revenue is equal to: 1 p*q= 1 q q q q 2 Thus the marginal revenue equals MR = 1 1 1 R 2 = q q q p q q We are considering an industry with increasing returns to scale, which implies the presence of fixed costs. Suppose that total costs are C = F + cq where F = fixed costs, those independent of the level of output c = the variable cost. The marginal cost is MC C c q The average cost is AC= C F c q q It is clear that as the quantity produced increases the average cost decreases. A larger firm is more efficient because average cost decreases as q increases this means that there are internal economies of scale. If we plot marginal cost and average cost we have: 1 Thus in monopoly we have that the equilibrium can be represented as follows: 2 As in any market structure, the profit-maximizing output occurs where marginal revenue equals marginal cost. MR=MC At the intersection of the MC and MR curves, the revenue gained from selling an extra unit equals the cost of producing that unit. The monopolist earns some monopoly profits, when P > AC. They are represented by the shaded box. We have an oligopoly when: -there are few firms in the market, which are able to affect prices -none of them has an uncontested monopoly When there are few actors in the market, their pricing policies are interdependent. In oligopoly each firm considers the responses of consumers in setting the price. This is far more complicated to analyze, so we skip this model and we move to another form of imperfect competition: Monopolistic competition. This is a simple model of an imperfectly competitive industry that assumes that each firm –can differentiate its product from the product of competitors (remember the love for variety Hp) –takes the prices charged by its rivals as given (price taker). A firm in a monopolistically competitive industry is expected: -to sell more the larger the demand in the industry -to sell more as prices charged by rivals increase. -to sell less as the number of firms in the industry increases -to sell less as the firm’s price increases. We summarize this in one function, which is the demand for the single firm: q = S[1/n – b(p – p )] q = an individual firm’s sales S = total sales of the industry n = number of firms in the industry b = a constant term representing the responsiveness of a firm’s sales to its price p= price charged by the firm itself p = average price charged by its competitors Assume that firms are symmetric: all firms face the same demand function and have the same cost function, thus all firms should charge the same price, they will have equal share of the market. p= p 3 q = S[1/n – b(p – p )] q = S/n We have this demand function: q = S[1/n – b(p – p )] We need to get the MR to determine the equilibrium. Let’s recall that given a linear demand function q=α-βp where α and β are constants. When firms maximize profits, they produce until marginal revenue equals marginal cost: MR = p 1 q So in this case we can write the production function as q= S Sbp Sb p n If we rearrange we get: S q = Sb p Sbp n where we can write that S Sb p n Sb This implies that the can retrieve MR easily MR = p 1 q So if we substitute for this demand equation we get MR = p 1 q =c=MC Sb If we rearrange we get: p c 1 q Sb Then we further manipulate. Knowing that q = S/n when all firms are equal, we can plug this into the equation and we get p c 1 bn 4 So we get the relationship between the number of firms and the price charged by each firm in equilibrium. This is a downward sloping curve: as the number of firms n ↑ in the industry increases, the price that each firm charges decreases because of increased competition. We need to add another equation in the model, that relates number of firms and the average costs. In this model the average costs should depend on the size of the market and the number of firms. To do this, we modify the expression for the average cost. We know that if all firms are symmetric we can write: q = S/n . We substitute this in the AC and get: AC = C/q = F/q + c AC = n(F/S) + c As the number of firms n ↑ in the industry increases, the average cost increases for each firm because each produces less. As total sales S ↑ of the industry increase, the average cost decreases for each firm because each produces more. This is an upward sloping schedule. We can now represent the equilibrium in a Monopolistically Competitive Market We now have to determine the number of firms n and the price of equilibrium p In equilibrium we have that the price that firms charge (which decreases in n) matches the average cost that firms pay (which increases in n). 5 In the long-run equilibrium number of firms in the industry, firms have no incentive to enter or exit the industry. However, we might be outside the equilibrium. Suppose we are in n1: firms have an incentive to enter the industry because price > average cost. Suppose we are in n2: firms have an incentive to exit the industry because price < average cost. Thus the market structure converges over time to the equilibrium with n2 What happens with trade? trade increases market size, in other words trade decreases the average cost in an industry described by monopolistic competition. AC = n(F/S) + c This curve is affected. The slope decreases (because S ↑) and the intercept is unchanged Trade increases the variety of goods. Consumers can buy more varieties and this increases the welfare of consumers, because average costs decrease, consumers can also benefit from a decreased price. What happens to the PP curve? It is unaffected as S does not enter this equation As a result of trade, the number of firms in a new international industry is predicted to increase relative to each national market. Notice however that the overall number of firms in the two economies will shrink, but it is unclear if firms will locate in the domestic country or foreign countries. Integrating markets through international trade therefore has the same effects as growth of a market within a single country. 6
