Frank Cowell Microeconomics November 2006 Exercise 3 3

Frank Cowell: Microeconomics November 2006 Exercise 3. 3 MICROECONOMICS Principles and Analysis Frank Cowell

Ex 3. 3(1) Question Frank Cowell: Microeconomics n n purpose: to derive competitive supply function method: derive AC, MC

Ex 3. 3(1) Costs Frank Cowell: Microeconomics n Total cost is: F 0 + ½ aqi 2 Marginal cost: aqi Average cost: F 0/qi + ½ aqi n Therefore MC intersects AC where: n This is at output level q where: n At this point AC is at a minimum p where: n For q below q there is IRTS and vice versa n n

Ex 3. 3(1) Supply Frank Cowell: Microeconomics n If p > p the firm supplies an amount of output such that u n If p < p the firm supplies zero output u n otherwise the firm would make a loss If p = p the firm is indifferent between supplying 0 or q u n p = MC in either case firm makes zero profits To summarise the supply curve consists of :

Ex 3. 3(1): Supply by a single firm Frank Cowell: Microeconomics §Average cost p §Marginal cost §Supply of output q qi

Ex 3. 3(2) Question Frank Cowell: Microeconomics n n purpose: to demonstrate possible absence of equilibrium method: examine discontinuity in supply relationship

Ex 3. 3(2): Equilibrium? Frank Cowell: Microeconomics §AC, MC and supply of firm p §Demand, low value of b §Demand, med value of b §Demand, high value of b Solution for high value of b is where Supply = Demand AC § MC ly Supp rm) fi (one qi

Ex 3. 3(2) Equilibrium Frank Cowell: Microeconomics n Outcome for supply by a single price-taking firm High demand: unique equilibrium on upper part of supply curve 2. Low demand: equilibrium with zero output 3. In between: no equilibrium 1. n Given case 1 “Supply = Demand” implies n This implies: n But for case 1 we need p ≥ p u from the above this implies

Ex 3. 3(3) Question Frank Cowell: Microeconomics n n purpose: to demonstrate effect of averaging method: appeal to a continuity argument

Ex 3. 3(3) Average supply, N firms Frank Cowell: Microeconomics n Define average output n Set of possible values for average output: n Therefore the average supply function is

Ex 3. 3(3) Average supply, limit case Frank Cowell: Microeconomics n As N the set J(q) becomes dense in [0, q] n So, in the limit, if p = p average output can take any value in [0, q] n Therefore the average supply function is

Ex 3. 3(3): Average supply by N firms Frank Cowell: Microeconomics §Average cost (for each firm) §Marginal cost (for each firm) p §Supply of output for averaged firms q q

Ex 3. 3(4) Question Frank Cowell: Microeconomics n n purpose: to find equilibrium in large-numbers case method: re-examine small-numbers case

Ex 3. 3(4) Equilibrium Frank Cowell: Microeconomics n Equilibrium depends on where demand curve is located u n High demand u n characterise in terms of (price, average output) equilibrium is at (p, p/a) where p = a. A / [a+b] Medium demand equilibrium is at (p, [A – p]/b) u equivalent to (p, bq) where b : = a[A – p] / [bp] u Achieve this with a proportion b at q and 1–b at 0 u n Low demand u equilibrium is at (p, 0)

Ex 3. 3(4): Eqm (medium demand) Frank Cowell: Microeconomics §AC and MC (for each firm) §Supply of output (averaged) §Demand p §Equilibrium achieved by mixing firms at 0 and at q § 1 b here q* q q

Ex 3. 4: Points to remember Frank Cowell: Microeconomics n n Model discontinuity carefully Averaging may eliminate discontinuity problem in a large economy u n depends whether individual agents are small. Equilibrium in averaged model may involve identical firms doing different things u equilibrium depends on the right mixture