Long Run Analysis. Definition 3

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1 Long Run Analysis Long run: Each firm has time to change its input mix optimally: for each firm short and long run supply curve can be different (see digression on next slide) Unless profits are 0, firms enter or exit the market. Profit=0 P =AC. As in the short run, P =MC from profit maximization Definition 3 A perfectly competitive market is in long-run equilibrium if there are no incentives for profit-maximizing firms to enter or to leave the market. This will occur when (a) the number of firms is such that P =MC =AC and (b) each firm operates at the low point of its long-run average cost curve. (b) is a consequence of (a) and of the (implicit) assumption of increasing marginal costs. Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

2 Digression: Short VS Long Run Cost Curves In the short run SOME inputs are fixed (see ch 9, from page 270) In the long run all inputs are flexible Hence: In the short run the Rate of Technical Substitution does not have to be equal to the ratio of the input prices (Fig. 9.12) The long run total cost curve is the lower than any short run total cost curve (any= for any level of the fixed input) (Fig 9.13) Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

3 Long Run: Constant Cost Entry or exit of firms affects the demand for inputs hence can affect the input prices. Simplest case: constant prices of inputs: E.g. the industry is a small fraction of the total demand of inputs With constant input prices, the long-run supply curve is horizontal. Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

4 Long Run: Constant Cost To understand why the long-run supply curve is horizontal: Let the demand increase, then: The short-run supply is an increasing curve, so the equilibrium price increases Firms earn a positive profit In the long run, new firms enter because of positive profits, causing increase in supply and reduction in price and profit BUT: by assumption, no effect on input prices Entry continues as long as firms earn positive profits, that is, as long as the price is above the original one. Note: in the short-run the supply curve is determined by the short-run marginal cost curve. In the long run, it is the low point of the long-run average cost curve that determines the supply curve Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

5 Long Run: Increasing Cost & Supply Curve Very common case: entry of new firms drives up price of inputs. Then the long-run supply curve is upward sloping In this case, if the demand increases, then: As the short-run supply is increasing, the equilibrium price increases Firms earn a positive profit In the long run, new firms enter because of positive profits, causing an increase in supply and reduction in price and profit, and an increase in input prices Entry continues as long as firms earn positive profits. The new long run equilibrium will have: (a) a higher price of the good, (b) more firms in the market and (c) a higher price of input (Note: (a) increases individual firms profits, while (c) decreases them, in the long run equilibrium (a) and (c) compensate each other) Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

6 Classification of Long Run Supply Curves To summarize, an industry supply curve exhibits one of three shapes. Constant costs: entry does not affect input costs; the long-run supply curve is horizontal at the long-run equilibrium price Increasing Costs: Entry increases input costs; the long run supply curve is positively sloped Decreasing Costs: Entry reduces input costs; the long run supply curve is negatively sloped Examples of decreasing costs: entry of new firms allows to reach a "critical size" of the industry sufficient to finance infrastructure that enhances productivity (either with money from the firms, or with public funding) Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

7 Producer Surplus in the Long Run In the short run, producer surplus represents the return to a firm s owners in excess of what would be earned if the output were 0. In the long-run: fixed-costs=0, profits=0, firm owners are indifferent to be in an industry or doing other economic activities In the long-run, sellers of inputs are NOT indifferent to the level of production in an industry. With increasing long-run supply curve, the producer surplus does not go to firm owners: it goes to input sellers. Graphically, the producer surplus in the long run can be found in the same way as the producer surplus in the short run Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

8 Welfare Analysis The market equilibrium maximizes the sum of consumer and producer surplus (graphical). See book p. 332, where last = in equation (11.59) should be -. Messing with the market equilibrium generally reduces welfare. Example 1: price control Help consumers & keep market price down transfers surplus from produces to consumers But: reduces overall surplus Can even reduce consumer surplus shortage (disequilibrium), black markets,... See blackboard Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

9 Welfare Analysis Example 2: tax t Tax added to sales price Producer price P S Consumer price P D Equilibrium condition: See blackboard slopes matter for deadweight loss who loses how much D(P D )=S(P S )=S(P D t) Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

10 Welfare Analysis Example 2 continued: tax incidence analysis i. A small change in the tax: consumer price Equilibrium condition: D(P D )=S(P S )=S(P D t) Differentiate with respect to the tax D P dp D dt =S P dp D dt S P, dp D dt = S P e S,P = (1) S P D P e S,P e Q,P Consumer price response to the tax as a function of the price elasticities of demand and supply. Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

11 Welfare Analysis Example 2 continued: tax incidence analysis i. A small change in the tax: producer price Similarly from differentiating D(P S +t)=d(p D )=S(P S ) dp S dt = e Q,P e S,P e Q,P (2) Dividing equation (1) over equation (2) yields dp S dt dp D dt = e Q,P e S,P (3) The relative price response of producer over consumer price is determined by ratio of the demand over the supply elasticity. Actor with less elastic response takes the higher price change. Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

12 Summary of Partial Equilibrium Analysis What have we learned? Short-run equilibrium: Price regulates demand and how much given firms produce long run equilibrium: # of firms varies, no profits, P =MC =AC. In long run, profits only occur through input price changes consumer & producer surplus maximized in market equilibrium surplus & deadweight loss for different regulations relation between elasticities and equilibrium price changes Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32

13 Limits of Partial Equilibrium Analysis A partial equilibrium analysis misses some effects of changes in technologies/preferences, for example: If overall income or the distribution of income changes, then demand for substitutes and complements changes, and with it the price of substitutes/complements, which in turn also affects the demand of the good considered If supply shifts because of a change in technology, the demand for inputs changes, and with it the price of inputs, which in turn affects supply of final good (in addition to original change in technology) Limited possibility to make a general statement about welfare as we always just see one market. Piacquadio & Traeger: Equilibrium, Welfare, & Information. UiO Spring /32