Tutorial 3 - Sessions 6to8:

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1 Simona Abis Tutorial 3 - Sessions 6to8: Session 7 - Pricing with market power: Essentials: Firms have market power, hence face downward sloping demand curves They can influence market price Charging a higher price they will be able to sell a lower quantity Trade off marginal revenue and volume The profit maximizing quantity is lower than the socially efficient quantity Condition for profit maximization: MR(Q) = MC(Q) No market power: Revenue = R(Q) = P*Q With market power: R(Q) = P(Q)*Q Special cases: Linear: Q = A - B*P hence P(Q) = A/B - 1/B*Q and MC = constant Setting MR = MC we obtain: P* = (P + MC)/2 Power: Q = AP^(-B) and B > 1 Setting MR = MC we obtain P* = (B/(B-1))*MC Condition for efficiency (usual): MV(Q) = MC(Q) With long-run fixed costs: Pricing decisions are still made as explained above Compute the variable profit at the optimal price and quantity Decide to enter the market if (Variable Profit) > (Fixed Costs) Patents can assure positive variable profits after investment so incentivizing firms to invest, but it leaves them market power without allowing them to acquire all gains from trade. The firm will produce less than what would be socially efficient Graphically: :46:19 1/8 Sessions 3to8 - Tutorial 3 - Solutions (#8)

2 How to solve, plot and interpret: Exercise 1 - Understanding the difference between profit maximizing and socially efficient equilibria: Given a firm with market power, with a constant marginal cost MC = 10, facing the following demand curve: Q = 10-1/2P a. Compute the profit maximizing price and quantity by using both the marginal condition and the short-cut: :46:20 2/8 Sessions 3to8 - Tutorial 3 - Solutions (2/8)

3 b. Compute the socially optimal price and quantity: c. Plot the demand curve, the marginal cost curve and show the profit maximizing and socially efficient equilibria: d. Show on the graph: producer surplus, consumer surplus and deadweight loss e. Compute total gains from trade, consumer surplus and producer's profit in both cases. Is there a deadweight loss? If so, compute it. f. (Midterm Problem 8) Suppose a regulator imposes a price cap that is little below the monopolist's price. What is likely to happen to the deadweight loss? :46:20 3/8 Sessions 3to8 - Tutorial 3 - Solutions (3/8)

4 Session 8 - Elasticity of Demand: Esentials: Slope: dy/dx Elasticity: %dy/%dx Own-price elasticity of demand: - %dq/%dp If = 0, Perfectly Inelastic If < 1, Inelastic If > 1, Elastic If = 1, Unit-elastic If =, Perfectly elastic Cross-price elasticity of demand: %dq/%dps If > 0, Substitute If < 0, Complement Income elasticity of demand: %dq/%di If < 0, Inferior good If > 0, Normal good If > 1, Luxury good Arc Elasticity of demand: (Q2 - Q1)/0.5(Q2 + Q1) (P2 - P1)/0.5(P2 + P1) Point Elasticity of demand: - (dq/dp)*(p/q) Special cases: Linear: Q = A - BP, E = P/(P - P) Power: Q = AP^(-B), E = B Why? Why do we use them? Linear: simple algebraic and graphical illustrations Power: for empirical estimation Connection with profit maximization: :46:21 4/8 Sessions 3to8 - Tutorial 3 - Solutions (4/8)

5 How to solve, plot and interpret? Exercise 1 - Understanding elasticity: Given the following demand curve and points on the curve, compute: a. The slope of the curve b. The arc elasticity using the High and Low price points c. The point elasticity at all given points Then plot the demand curve and show where the demand is inelastic, elastic, unit-elastic, perfectly elastic and inelastic :46:21 5/8 Sessions 3to8 - Tutorial 3 - Solutions (5/8)

6 Problem 2 - Midterm 2008: Which of the following statements about elasticity of demand are true? a. If two goods are substitutes, then their cross-price elasticity is negative b. A steeper demand curve is less elastic than a flatter demand curve Problem 4 - Midterm 2008: Your regression on demand for gasoline yielded the following coefficients: log(g) = log(PG) log(Y) log(PNC) log(PUC) Here, G is per-capita consumption of gasoline and Y is per-capita income. According to these results, which of the following are true? a. Gasoline is a normal good b. Gasoline is a luxury good c. Demand for gasoline is elastic :46:22 6/8 Sessions 3to8 - Tutorial 3 - Solutions (6/8)

7 Problem 17 - Exam 2008 Consider the following graph of two linear demand curves: Let Ea be the point elasticity of demand curve d2(p) at the point marked and let Eb and Ec be the elasticities of the demand curve d1(p) at the points marked. Answer the following questions assuming that you only know that the curves are drawn "this way", but without trying to calculate elasticities by measuring with a ruler. a. Do you have enough information to tell whether Ea > Eb or Ea < Eb? Explain. b. Do you have enough information to tell whether Eb > Ec or Eb < Ec? Problem 14 -Exam 2011: Consider a firm with market power that has constant marginal cost. Its current demand curve d1(p) and its profit maximizing price and quantity are P1 and Q1, respectively. The demand curve shifts to d2, which is less elastic than d1. Yet d1 and d2 intersect at the point (Q1, P1). a. Draw a graph that illustrates this situation, using linear demand. Your graph has to show: d1, d2 and the intersection point (Q1, P1) :46:22 7/8 Sessions 3to8 - Tutorial 3 - Solutions (7/8)

8 b. What happens to the quantity sold following the shift in demand? :46:22 8/8 Sessions 3to8 - Tutorial 3 - Solutions (8/8)