**JUNK** (no subject)

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**JUNK** (no subject)

  1. 1. Total and Marginal Revenue
  2. 2. Total and Marginal Revenue
  3. 3. Quantity Demanded MR/Price -10 -5 0 5 10 0 2 4 6 8 10 12 Marginal Revenue Average Revenue Total Revenue 0 5 10 15 20 25 30 35 0 2 4 6 8 10 12 Quantity per period Total Revenue 15
  4. 4. Marginal Revenue Equation <ul><li>Demand Equation Q = B + a p P </li></ul><ul><li>P = -B/a p + Q/a p </li></ul><ul><li>TR = PQ = -B/a p *Q + Q 2 /a p </li></ul><ul><li>MR = d(PQ)/dQ = -B/a p + 2Q/a p </li></ul><ul><li>MR = 0 , Q = B/2 </li></ul><ul><li>For Q < B/2 , MR = +ve Q > B/2 , MR = -ve </li></ul>
  5. 5. Relation of Demand & Marginal Revenue Curve <ul><li>The curves intercept y-axis at same point </li></ul><ul><ul><li>Intercept of MR & Demand (DD) curve = -B/a p </li></ul></ul><ul><li>Slope of (DD) curve = 1/ a p </li></ul><ul><li>Slope of MR curve = 2/ a p = 2 DD curve </li></ul>
  6. 6. ELASTICITY <ul><li>A general concept used to quantify the response in one variable when another variable changes </li></ul><ul><li>elasticity of A with respect to B = </li></ul><ul><li>%  A/ %  B </li></ul>
  7. 7. Calculating Elasticities Pounds of X per month Slope:  Y = P 2 – P 1  X = Q 2 – Q 1 = 2 – 3 = -1 10 – 5 = 5 Ounces of X per month Slope:  Y = P 2 – P 1  X = Q 2 – Q 1 = 2 – 3 = -1 160 –80 = 80 P P 0 P 1 = 3 P 2 = 2 Q 1 = 5 Q 2 = 10 D Price per Pound Pounds of X per week P 1 = 3 P 2 = 2 Q 1 = 80 Q 2 = 160 D Price per Pound Ounces of X per week Q Q 0
  8. 8. Point Price Elasticity of Demand Point Definition Ratio of the percentage of change in quantity demanded to the percentage change in price. %  Q Ep = %  P
  9. 9. For  P approaching 0  Q/  P = dQ/dP Linear equation = dQ/dP = constant dQ/dP = a p Q d = B + a p P = B + dQ/dP P Point Price Elasticity of Demand
  10. 10. Point Price Elasticity of demand 0 1 2 3 4 5 6 7 0 100 200 300 400 500 600 700 Qx Px A F G H J B C Dx
  11. 11. <ul><li>B = -5 </li></ul><ul><li>C = -2 </li></ul><ul><li>F = -1 </li></ul><ul><li>G = -0.5 </li></ul><ul><li>H = -0.2 </li></ul>
  12. 12. Arc Price Elasticity of Demand E p = Q 2 - Q 1 P 2 - P 1 (Q 2 + Q 1 )/2 (P 2 + P 1 )/2
  13. 13. Example <ul><li>Calculate the arc price elasticity from point C to point F. </li></ul><ul><li>= (300 – 200)/ (3-4) * ((3+4)/ (300+200)) </li></ul><ul><li>= -1.4 </li></ul>
  14. 14. Calculate Elasticity
  15. 15. Total Marginal Elasticity
  16. 16. Marginal Revenue and Price Elasticity of Demand MR = d(PQ) = dQ*P + dP*Q dQ dQ dQ = P + QdP = P 1 + dP.Q dQ dQ P
  17. 17. Quantity Demanded MR/Price -10 -5 0 5 10 0 2 4 6 8 10 12 Marginal Revenue Elastic Ep < - 1 Unitary elastic Ep = - 1 Inelastic -1 < Ep < 0 Total Revenue 0 5 10 15 20 25 30 35 0 2 4 6 8 10 12 Quantity per period Total Revenue 15
  18. 18. <ul><li>Perfectly inelastic demand </li></ul><ul><ul><li>Q d does not change at all when price changes </li></ul></ul><ul><li>Inelastic demand </li></ul><ul><ul><li>-1 < E  0 </li></ul></ul><ul><li>Unitary elastic demand </li></ul><ul><li>E = -1 </li></ul><ul><li>Elastic demand </li></ul><ul><ul><li>E < -1 </li></ul></ul><ul><li>Perfectly elastic demand </li></ul><ul><ul><li>Q d drops to zero at the slightest increase in price </li></ul></ul>
  19. 19. Price Qty Demanded 0 Q P Price Qty Demanded 0 Q P D D Perfectly Inelastic Demand Perfectly Elastic Demand
  20. 20. <ul><li>P * Q d = TR Elastic Demand </li></ul><ul><li>P * Q d = TR Elastic Demand </li></ul><ul><li>P * Q d = TR Inelastic Demand </li></ul><ul><li>P * Q d = TR Inelastic Demand </li></ul>
  21. 21. Present Loss : $ 7.5 million Present fee per student : $3,000 Suggested increase : 25% Total number of students : 10000 Elasticity for enrollment at state universities is -1.3 with respect to tuition changes 1% increase in tuition = 1.3% decrease in enrollment Increase of 25% decline in enrollment by 32.5% 3000 * 10000 = $30,000,000 3750 * 6750 = $25,312,500 Problem
  22. 22. Determinants of Price Elasticity of Demand <ul><li>Demand for a commodity will be less elastic if: </li></ul><ul><li>It has few substitutes </li></ul><ul><li>Requires small proportion of total expenditure </li></ul><ul><li>Less time is available to adjust to a price change </li></ul>
  23. 23. Determinants of Price Elasticity of Demand <ul><li>Demand for a commodity will be more elastic if: </li></ul><ul><li>It has many close substitutes </li></ul><ul><li>Requires substantial proportion of total expenditure </li></ul><ul><li>More time is available to adjust to a price change </li></ul>
  24. 24. Income Elasticity of Demand Point Definition The responsiveness of demand to changes in income. Other factors held constant, income elasticity of a good is the percentage change in demand associated with a 1% change in income
  25. 25. Income Elasticity of Demand Arc Definition
  26. 26. Demand of automobiles as a function of income is Q = 50,000 + 5(I) Present Income = $10,000 Changed Income = $11,000 I 1 = $10,000, Q = 100,000 I 2 = $11,000, Q = 105,000 E I = 0.512
  27. 27. <ul><li>Normal Goods ΔQ/ΔI = +ve, E I = +ve </li></ul><ul><ul><li>Necessities 0 < E I  1 </li></ul></ul><ul><ul><li>Luxuries E I > 1 </li></ul></ul><ul><li>Inferior Goods ΔQ/ΔI = -ve, E I = -ve </li></ul>
  28. 28. Cross-Price Elasticity of Demand Point Definition Responsiveness in the demand for commodity X to a change in the price of commodity Y. Other factors held constant, cross price elasticity of a good is the % change in demand for commodity X divided by the % change in the price of commodity Y
  29. 29. Cross-Price Elasticity of Demand Arc Definition Substitutes Complements
  30. 30. Importance of Elasticity in Decision making <ul><li>To determine the optimal operational policies </li></ul><ul><li>To determine the most effective way to respond to policies of competing firms </li></ul><ul><li>To plan growth strategy </li></ul>
  31. 31. Importance of Income Elasticity <ul><ul><li>Forecasting demand under different economic conditions </li></ul></ul><ul><ul><li>To identify market for the product </li></ul></ul><ul><ul><li>To identify most suitable promotional campaign </li></ul></ul>
  32. 32. Importance of Cross price Elasticity <ul><ul><li>Measures the effect of changing the price of a product on demand of other related products that the firm sells </li></ul></ul><ul><ul><li>High positive cross price elasticity of demand is used to define an industry </li></ul></ul>
  33. 33. Problem <ul><li>Qx = 1.5 – 3.0P x + 0.8I + 2.0P y – 0.6P s + 1.2A </li></ul><ul><li>P x =$2 I=$2.5 P y =$1.8 </li></ul><ul><li>P s =$0.50 A=$1 </li></ul><ul><li>Qx =1.5 – 3*2 + 0.8*2.5 + 2*1.8 – 0.6*0.50 + 1.2*1 </li></ul><ul><li>=2 </li></ul><ul><li>E p = -3(2/2) = -3 E I = 0.8(2.5/2) = 1 </li></ul><ul><li>E xy = 2(1.8/2) = 1.8 E xs = -0.6(0.50/2) = -0.15 </li></ul><ul><li>E A = 1.2(1/2) = 0.6 </li></ul>
  34. 34. <ul><li>Next Year: </li></ul><ul><li>P=5% A=12% I=4% Py=7% Ps=8% </li></ul>Q’x =2.2
  35. 35. Exercise <ul><li>A consultant estimates the price-quantity relationship for New World Pizza to be at P = 50 – 5Q. </li></ul><ul><ul><li>At what output rate is demand unitary elastic? </li></ul></ul><ul><ul><li>Over what range of output is demand elastic? </li></ul></ul><ul><ul><li>At the current price, eight units are demanded each period. If the objective is to increase total revenue, should the price be increased or decreased? Explain. </li></ul></ul>
  36. 36. <ul><li>P =50 -5Q </li></ul><ul><li>MR = 50-10Q </li></ul><ul><li>For unitary elastic MR = 0 so Q =5 </li></ul><ul><li>MR will be +ve when Q<5, so demand will be elastic when 0<=Q<5. </li></ul><ul><li>P for Q=8 is P=50-5*8 = 50-40 = 10 </li></ul><ul><li>Ep= -1/5*10/8 = -0.25. As demand is inelastic, when we increase price, TR increases. </li></ul>
  37. 37. Exercise <ul><li>For each of the following equations, determine whether the demand is elastic, inelastic or unitary elastic at the given price. </li></ul><ul><ul><li>a) Q =100 – 4P and P = $20 </li></ul></ul><ul><ul><li>b) Q =1500 – 20 P and P = $5 </li></ul></ul><ul><ul><li>c) P = 50 – 0.1Q and P = $20 </li></ul></ul><ul><li>-4, elastic </li></ul><ul><li>-0.07, Inelastic </li></ul><ul><li>-0.67, Inelastic </li></ul>

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