2- Demand and Engel Curves derive from consumer optimal choice problem: = PL

Transcription

1 Correction opics -he values of the utility function have no meaning. he only relevant property is how it orders the bundles. Utility is an ordinal measure rather than a cardinal one. herefore any positive monotonic transformation of a function does not change the function value ordering and the transformed utility function represents the same preferences. U (, L) 0,3 0,7 0,3ln L + 0,7ln and U (, L) L represent the same preferences. - Demand and Engel Curves derive from consumer optimal choice problem: PL 0,7L P M PL L + P 3 0,7L P 0,3 0 P + P 0,7 70 0,7M Demand curve P P Engel curve M Graphs 0,3M L P 3- L 0. Cross elasticity is zero, neither demand P L P L substitutes nor demand complements. 4- he compensated demand function relates how the quantity demanded change when the price of the good changes keeping the level of utility constant. 3 PL 0,7 0,3 0,7 L P P L P 0,3 0,3 0,7 0,3 0,3 P U L U ( ), Compensated demand functions are always decreasing relations. 5-0, 3 { ( ) 0,7, PL 0,7L P M PL L + P L M ' 6* + 7 * 30 For Mr. Jobs the subsidy necessary to maintain consumption is S30, M -M. his value corresponds to the Slutsky Compensating Variation.

2 6-6 0,7L L + 7 L L 6,5 30 6L + 4L 3 he consumers will always adjust its consumption bundle taking into account the new relative prices. With Slutsky Compensating Variation initial bundle is no longer an optimal choice. he new optimal choice is in a higher indifference curve. Utility increases. Consumers are over compensated. 7- If relative prices are maintained and income is adjusted with consumer price index, decision variables are kept in real terms and consumer choice is not affected. If relative prices change, adjusting wages with consumer price index is equivalent to Slutsky compensating variation. Slutsky compensating variation overcompensates consumers for a change in relative prices. See graph x D Consumer Price Index, CPI B F I o x

3 II - Long run cost function represents the least cost to produce any amount of production given technology and input prices. he long-run cost function derives from optimal input choice model of a producer. 0,5K 0,5L K L C L + K { C 0Y 0,5 0,5 Y K L Y K L No, this production function has constant returns to scale. If doubling K and L, Y is doubled. 0,5 0,5 Y (K ) (L) - A competitive market is in long run equilibrium when price is equal to long run marginal cost (optimal firm choice) and equal to the minimum average cost ( no entry and exit of firm) With this long run cost function, average costs are not U shaped they are constant and always equal to Marginal costs, MCAC0. Market long run Equilibrium price is Changing input relative prices will change optimal input choices for any level of production. he expansion path is shifted. In this case, increasing the price of capital will induce substitution from capital to labor. his will decrease the capital labor ratio of the expansion path. K L

4 4-0,5K 0,5L 40 C L + 40K 0,5 0,5 Y K L K L 4 0,5 Y L 4 0,5 L 0,5 K L 4 Y L Y K { C 0Y + 0Y 40Y Firms have huge losses, most shut down, supply decreases, prices start to rise until price is equal to 40. III - Monopoly market equilibrium. (0 Q) Q 40Q - 0 Q 40 Q 30; P 70 π CS 450 PS 900 o maximize welfare PMC, therefore P40 and Q60. At this price CS + PS are maximized but firm suffer losses of 400. wo possible efficient pricing policies: a) Maximum price limit - P 40 and government support losses b) wo part tariffs: P40 and access tariffs A400/number of clients 3- Q 60; P 40 π CS 800 PS 0 he maximum society is willing to pay for having a Regulatory Agency is the gain in welfare due to regulatory intervention

5 4- Cournot duopoly (0 Q Q 0 Q Q 0 Q (0 Q Q Q ) Q 40 Reaction function of firm ) Q 40Q 40Q 40 Reaction function of firm Q 0; Q 40P 60 π π Q CS 800 PS 0 5- Stakelberg duopoly- Firm is the leader (0 Q Q subject to Q 30 Q Reaction function of firm 0 Q 30 + Q 40 Q 30 Q 5; Q 45P 55 π π CS,5 PS 675 ) Q 40Q IV - he statement is correct. No firm will continue to produce and sell in the long run supporting permanent losses. P AC is the same as P * Q AC*Q and the same as otal Revenues equal otal Costs - he statement is wrong. he optimal decision rule for a competitive firm is to produce and sell quantities where price equals Marginal Costs. his is the profit maximizing rule. Choosing Q that Max π P *Q C * (Q) implies by the first order condition of this maximization problem P MC Entry and exit of firms will drive the equilibrium to the level of production where P MC Min AC

6 V-

7 VI-