Econ 104 Welfare Analysis PDF

LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 10: Welfare Analysis LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: discuss measures of welfare cha...

LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez ECONOMICS 104 Topic 10: Welfare Analysis LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: discuss measures of welfare change among economic agents analyze welfare changes as a result of various market distortions explain the concepts of compensating and equivalent variation as measures of welfare change 1 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez MEASURES OF WELFARE CHANGES Consumers changes in utility levels Firms changes in profits/economic rent Government changes in budget (from tariff or tax revenue) Society consumers and firms (and government) LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez CONSUMERS Consumer Surplus (CS) The difference between the consumers total willingness to pay (TWP) and actual payments or total expenditures (TE) CS  TWP  TE P P CS CS P P D D Q Q0 Q 2 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Note: In measuring consumer surplus, we use the Hicksian Demand Curve Recall: Hicksian Demand Curve shows the relationship between the price of a commodity and the quantity demanded, holding other prices and utility constant Qd X  D( PX ; PY ,U ) Homework: Graphically derive the Hicksian Demand Curve LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez CS CHANGE RESULTING FROM PRICE CHANGES Compare CS before and after the price change. Suppose P increases from P1 to P2 P P2 Decrease in CS P1 D Q 3 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez PRODUCERS Producer Surplus (PS) The difference between the producers total revenue (TR) from selling their product and their willingness to sell the product or at the least, the total variable cost (TVC) PS  TR  TVC P S P S PS PS P P Q Q0 Q LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Note: In the short-run, as long as economic rent is not negative, then the firm can still continue on its production to minimize losses (if profit is negative) ER  TR  TVC  PS Recall: The firm’s supply curve is the rising portion of the MC curve above the minimum of the AVC curve MC, MC = S AVC AVC Q 4 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Thus, the marginal cost can be used as basis for measuring the PS Recall: TC  X   TVC  X   F dTC  X  dTVC  X  dF MC X    dX dX dX 0 dTC  X  dTVC  X  MC X   dX dX Note: The area under the MC curve is the Total Variable Cost (via integration) LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez VC  X   differentiation MC  X  VC  X   integration MC  X  (area under the curve) Graphically: MC MC MC =PS S P0 ER TR TVC TVC X0 X X0 X 5 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez PS CHANGE RESULTING FROM PRICE CHANGES Compare PS before and after the price change. Suppose P decreases from P1 to P2 P S P1 Decrease in PS P2 Q LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez GOVERNMENT Government may collect taxes or tariff to generate revenues This revenues can be looked at as part of the societal welfare since it can be redistributed to consumers and/or producers which will increase their welfare Thus, the revenues can be added as part of measuring societal welfare 6 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez SOCIETY CS + PS + Revenues Suppose, no government intervention: P S CS Societal P Welfare PS D Q LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez WELFARE APPLICATIONS We now analyze welfare changes from market distortions Price ceiling Floor price Price support Taxation Specific tax Lump-sum tax 7 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez PRICE CEILING Imposed to make a commodity more affordable P S DWL P* PC D Q Q LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez FLOOR PRICE imposed so that prices do not fall below a certain minimum level P S PF DWL P* D Q Q 8 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez PRICE SUPPORT government commits to buy all excess supply leads to budget deficit (welfare loss in the part of the government) the excess supply bought can then be stored At times of crisis, these stored excess supply can be made available This mechanism can be used to prevent adverse price changes (shocks) LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez PRICE SUPPORT government buy all excess supply P Welfare S Gain PS P* P* D 9  LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez TAXATION generates revenue for the government most taxes created distortions that leads to DWLs Recall: Tax revenues can be looked at as part of the societal welfare (gain in societal welfare) since it can be redistributed to consumers and/or producers which will increase their welfare LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez P Specific Tax St Tax shifts the supply a S curve to the left, i.e. to St, decreasing output to Xt Tax creates a gap c between price paid PC by the consumers (PC) and the take- t P* e home price of producers (PP) PP CS: aPCc d PS: bPPd ΔCS: (PCP*ec) ΔPS: (PPP*ed) b D Tax rev: PPPCcd SW: abdc 0 Xt X* X DWL: cde 10 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez LUMP-SUM TAX Flat tax Does not cause distortion This mechanism simply reallocates some of the economic rent received by the producers to the government via taxes. LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Try this! Do the welfare analysis with the following given functions: Hicksian Demand Function: Q = 50 – 0.5P Total Cost Function: C= 0.25Q2 + 25Q + 100 Note: The supply curve can be derived from the TC via the MC curve 11 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez EXTENSION: WELFARE ANALYSIS WITH NON-LINEAR FUNCTIONS Recall: P CS  TWP  TE Q0 CS TWP   D(Q)dQ 0 P0 TE  P0  Q0 D Q0 Q Thus: Q0 CS   D(Q)dQ  P  Q 0 0 0 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez EXTENSION: WELFARE ANALYSIS WITH NON-LINEAR FUNCTIONS Recall: S P PS  TR  TVC PS TR  P0  Q0 P0 Q0 TVC   S (Q)dQ 0 Q0 Q Thus: Q0 PS  P0  Q0   S (Q)dQ 0 12 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Example: D : P  f (Q) P0  100  Q0  30 P  1000  Q2 Solving for CS CS  TWP  TE 30 TWP   (1000  Q 2 )dQ 0 30 TWP  (1000Q  1 3 Q  c)3 0 TWP  [(1000)(30) 1 3(30)3  c]  [0  c]  21000 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez TE  (100)(30)  3000 Thus: CS  21000  3000  18000 Try this! Solve for the PS at P0 =100 given the cost function: C  1 3 Q3  1 2 Q2  10Q  100 Try this! Verify the CS and PS for the linear supply and demand function case using this procedure 13 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez COMPENSATING VARIATION Compensating Variation Point of reference: original IC Consider a price increase: The CV is the amount of money that must be given to an individual so as to leave him just as well off as he was before the rise in the price The rise in price would shift the IC to the left. The CV then measures a hypothetical amount of money that should be given to the individual for him to return to the original IC considering the price change LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Y Recall: Hicksian vs. B Marshallian Y1 A Demand Y0 = Y2 C Curves U Suppose P U’ increases X2 X1 X0 X PX from P0 to P1 P1 P0 hX dX X2 X1 X0 X 14  LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez How much money should be Y given to the individual to be able to reach the original IC? CV Increase in income shifts the budget line which makes the original IC attainable B Y1 PX A Y0 = Y2 P1 C CV U P0 U’ hX dX X2 X1 X0 X X2 X1 X0 X LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez EQUIVALENT VARIATION Equivalent Variation Point of reference: new IC Consider a price increase: The EV is the amount of money that must be taken from an individual to make him as well off as he will be after the rise in the price The rise in price would shift the IC to the left. The EV then measures a hypothetical amount of money that should be taken from the individual for him to be at the new IC not considering the price change 15  LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez How much money should be Y taken from the individual to be at the new IC without the price change? Decrease in income shifts the budget line which makes the EV individual be at the new IC B Y1 PX A Y0 = Y2 P1 C EV U P0 U’ h‘X hX dX X2 X1 X0 X X2 X1 X0 X LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez Note: For a price increase: CV>CS>EV CV=CS=EV under a special type of utility function that does not exhibit income effect, i.e. quasilinear utility function Try this! Graphically illustrate the CV and EV for a price decrease. Also, interpret what does the CV and EV mean under this situation. 16 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez LEARNING OBJECTIVES At the end of the topic, the learners should be able to: discuss measures of welfare OR change among economic agents analyze welfare changes as a result OR of various market distortions explain the concepts of compensating and equivalent OR variation as measures of welfare change LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez REFERENCES Nicholson, W. and Snyder, C. 2007. Microeconomic Theory: Basic Principles and Extensions. 10th Ed., South-Western, Cengage Learning, pp 167-169, 371-374, 419-427 & 165-167. Varian, H. 2010. Intermediate Microeconomics: A Modern Approach, 8th Ed. New York: WW Norton and Co. Note: Learning resources can be accessed in our ECON 104 eLBI Course Site at http://ilcecourses.uplb.edu.ph/course/ 17 LMAT-A10 Learning Facilitator: Paul Joseph B. Ramirez END OF TOPIC 10 Topic 10: Welfare Analysis Next Topic: Social Choice Theory 18