Concepts from the Theory of the Firm

Transcription

1 Concepts from the Theor of the Firm Daniel Kirschen Universit of Manchester 2006 Daniel Kirschen 1

2 Production function = f ( x,x ) 1 2 : output x 1, x 2 : factors of production x 2 fixed x 1 fixed x 1 x 2 Law of diminishing marginal products 2006 Daniel Kirschen 2

3 Long run and short run Some factors of production can be adjusted faster than others Example: fertilizer vs. planting more trees Long run: all factors can be changed Short run: some factors cannot be changed No general rule separates long and short run 2006 Daniel Kirschen 3

4 Input-output function = f ( x 1, x 2 ) x 2 fixed The inverse of production function is the input-output function x 1 = g ( ) for x 2 = x 2 Example: amount of fuel required to produce a certain amount of power with a given plant 2006 Daniel Kirschen 4

5 Short run cost function c SR ( ) = w 1 x 1 + w 2 x 2 = w 1 g( ) + w 2 x 2 w 1, w 2 : unit cost of factors of production x 1, x 2 c SR ( ) 2006 Daniel Kirschen 5

6 Short run marginal cost function c SR ( ) Convex due to law of marginal returns dc SR ( ) d Non-decreasing function 2006 Daniel Kirschen 6

7 Optimal production Production that maximizes profit: max { π c SR ( ) } d{ π c SR ( ) } d = 0 π = dc SR ( ) d Onl if the price π does not depend on perfect competition 2006 Daniel Kirschen 7

8 Costs: Accountant s perspective In the short run, some costs are variable and others are fixed Variable costs: labour materials fuel transportation Fixed costs (amortised): equipments land Overheads Quasi-fixed costs Startup cost of power plant Sunk costs vs. recoverable costs Production cost [ ] Quantit 2006 Daniel Kirschen 8

9 Average cost c( ) = c v ( ) + c f AC( ) = c( ) = c v ( ) + c f = AVC ( ) + AFC ( ) Production cost [ ] Average cost [ /unit] Quantit Quantit 2006 Daniel Kirschen 9

10 Marginal vs. average cost /unit MC AC Production 2006 Daniel Kirschen 10

11 When should I stop producing? Marginal cost = cost of producing one more unit If MC > ϖ next unit costs more than it returns If MC < ϖ next unit returns more than it costs Profitable onl if Q 4 > Q 2 because of fixed costs π Average cost [ /unit] Marginal cost [ /unit] Q 1 Q 2 Q 3 Q Daniel Kirschen 11

12 Costs: Economist s perspective Opportunit cost: What would be the best use of the mone spent to make the product? Not taking the opportunit to sell at a higher price represents a cost Examples: Growing apples or growing kiwis? Use the mone to grow apples or put it in the bank where it earns interests? Includes a normal profit Selling at cost does not mean no profit 2006 Daniel Kirschen 12

13 Perfect competition Perfect competition The volume handled b each market participant is small compared to the overall market volume No market participant can influence the market price b its actions All market participants act like price takers Price Inframarginal suppl Extra-marginal demand Quantit Marginal producer 2006 Daniel Kirschen 13

14 Imperfect competition One or more competitors can influence the market price through their actions Strategic plaers Participants with a large market share Can influence the market price Competitive fringe Participants with a small market share Take the market price Cournot and Bertrand models of competition 2006 Daniel Kirschen 14

15 Cournot model in a duopol Competition on quantit Problem for firm 1: 1 = f 1 ( 2 e ) max 1 π ( e ) 1 c ( 1 ) Similar problem for firm 2 2 = f 2 ( 1 e ) * 1 = f 1 ( * 2 ) Cournot equilibrium: 2* = f 2 ( 1* ) Neither firm has an incentive to deviate from the equilibrium 2006 Daniel Kirschen 15

16 Cournot model in an oligopol Total industr output: Firm i: Y = max { i π (Y ) c ( i ) } i d d i π (Y ) c( i ) i 1 +L + n { } = 0 dπ (Y ) π (Y ) + i = dc ( i ) d i d i π (Y ) 1 + π (Y ) 1 i Y Y dπ (Y ) d i π (Y ) s i ε (Y ) = dc ( i ) d i = dc ( ) i d i Difference with perfect competition 2006 Daniel Kirschen 16

17 Cournot model in an oligopol π (Y ) 1 s i ε (Y ) < 1 = dc ( i ) d i Strategic plaer operates at a marginal cost less than the market price Abilit to manipulate prices is a function of: s i = i Y Market share Elasticit of demand ε 2006 Daniel Kirschen 17

18 Bertrand model in a duopol Competition on price Firm that sets the lowest price captures the entire market No firm will bid below its marginal cost of production because it would sell at a loss At equilibrium, both firms sell at the same price, which is the marginal cost of production Equivalent to competitive equilibrium! Not a realistic model! 2006 Daniel Kirschen 18