Evans Barasa

 Demand Elasticity Author’s Name: Institutional of Affiliation: Date WEEK 5 AssignmentsMG 640 Questions 1 1. Answer the following questions based on the accompanying diagram a. (i)How much would the firm’s revenue change if it lowered price from $16 to $14? Revenue is calculated by Multiplying Demand to price that is, Revenue (TR) = Demand (Q) X Price (P), therefore TR=QP Change in revenue is therefore calculated by multiplying change in Demand (ΔQ) X change in Prices (ΔP) ΔTR= (ΔQ) X (ΔP) At the price is $16, the demand level at point 2 Total Revenue1 is $16 X 2 = $ 32. At price level $14, the Demand level is at point 4 Total Revenue2 is $14 X 4 = $56. Revenue changes = Total revenue2- Total revenue 1 that is ($56-$32) Revenue change is $24. (ii)Is demand elastic or inelastic in this range? Using mid-point rule: % change is Quantity is {(16-14)/15} =2/15=13% or 0.13 And % change in price is {(4-2)/3} = 2/3= 66 % or 0.66 Price elasticity of demand (De) = % change in quantity /% change in price De=13/66 =0.197 Since 0.197 ˂1, the demand is inelastic. b. How much would the firm’s revenue have changed if it lowered price from $6 to $4? Is demand elastic or inelastic in this range? Once again, Total Revenue is calculated by Multiplying Demand to price that is, Revenue (TR) = Demand (Q) X Price (P), therefore TR=QP Change in revenue is therefore calculated by multiplying change in Demand (ΔQ) X change in Prices (ΔP) ΔTR= (ΔQ) X (ΔP) At the price is $6, the demand level at point 6 TR1 is $6 X 6 units = $ 36. At price level $4, the Demand level is at point 4 TR2 is $4 X 8 units = $32. Δ Revenue = TR2 - TR1 that is ($32-$36) Revenue change is -$4. c. What price maximizes the firm’s total revenue? i. The demand function is written as P=a-bQd, where “a” is the Y intercept, and “b” is the slope (gradient) of the curve. This can be re-written as P=a-()Qd . We will use points A to N By substituting the figures into the price equation, P=16 - )Qd that is P=16-(2)Qd Thus P=16-2Qd by making Q the subject, Qd=8 - , When P is substituted in the Total revenue Equation, TR=PQ, it gives, TR= (16-2Q) Q TR=16Q-2Q2 For maximization we will use TR against Q and equate to zero (0). That is… =0 giving us { } =0 (16-4Q) =0 Q= 4. This is the output that maximizes the firm’s revenue. By using the Price equation, P=16-2(4) That is P=8. The firm’s revenue is maximized when price is at point 8. ii. What is the elasticity of demand at this point on the demand curve? The price point demand elasticity is calculated using the below formula: Ed = { X }= ( X 2) that is - X2, making it = -1. The price elasticity of demand is -1 point on the demand curve. 2 4 5 6 8 10 2. Suppose the income elasticity of demand for good X is 2, its own price elasticity of demand is -4, its advertising elasticity is 3, and the cross-price elasticity of demand between it and good Y is -6. Determine how much the consumption of this good will change if: a. The price of good X increases by 2 percent EQx.px= that is -4 = = -8, this means if the price of good X increases by 2% , consumption will decrease by 8 percent . b. The price of good Y increases by 2 percent c. Epy= that is -6 = giving us -0.12. The consumption of good X will decrease by -0.12 d. Advertising decreases by 2 percent e. AED= If 3= That is -6% = f. Income falls by 2 percent Eyx= Given that Eyx is 2 and the % change is income is 2%, then the 2 = Therefore there will be 4 % increase in the consumption of commodity X, due to 2% increase in the income levels of the consumers. References Samuelson, W. F., & Marks, S. G. (n.d.). Managerial economics. Retrieved from http://s1.downloadmienphi.net/file/downloadfile7/149/-.pdf