Demand in the market for Gumble\'s Special Stuff is represented by the following
ID: 1105607 • Letter: D
Question
Demand in the market for Gumble's Special Stuff is represented by the following function: 1. P =-0.002 Qd + 120 where: P = price per unit in $ = quantity demanded in units per month. a) Calculate the own price elasticity of demand: i) for the change in price from $80 to $40 using startpoint/original quantities method li) for the change in price from $80 to $40 using midpoint/average quantities method ii) at the price of $80 for an infinitesimally small change iv) at the price of $40 for an infinitesimally small change v) at the price of $60 (= ½(40 + 80)) for an infinitesimally small change vi) Comment on your results. [10 marks] b) The firm is willing to sell 30,000 units at a price of $60 each, and 40,000 units at $80. i Determine the supply function for the firm, stating any assumptions you make. li) Calculate the equilibrium price and quantity in the market, and the revenue generated by the firm. [5 marks] [Total: 15 marks]Explanation / Answer
P = - 0.002Qd + 120
0.002Qd = 120 - P
Qd = 60,000 - 500P
(a)
When P = $40, Qd = 60,000 - (500 x 40) = 60,000 - 20,000 = 40,000
When P = $80, Qd = 60,000 - (500 x 80) = 60,000 - 40,000 = 20,000
(i) Start-point Elasticity = % Change in Qd / % Change in P
= [(20,000 - 40,000) / 40,000] / [$(80 - 40) / $40]
= (- 20,000 / 40,000) / ($40 / $40)
= - 0.5
(ii) Midpoint elasticity = (% Change in Qd / Average Qd) / (% Change in P / Average P)
= [(20,000 - 40,000) / (20,000 + 40,000) / 2] / [$(80 - 40) / $(80 + 40) / 2]
= [- 20,000 / (60,000) / 2] / [($40 / ($120 / 2)]
= (- 20,000 / 30,000) / ($40 / $60)
= - 1
(iii) When P = $80, Qd = 20,000
Elasticity = (dQd / dP) x (P / Qd) = - 500 x (80 / 20,000) = - 2
(iv) When P = $40, Qd = 40,000
Elasticity = (dQd / dP) x (P / Qd) = - 500 x (40 / 40,000) = - 0.5
NOTE: First 4 parts of the 1st question are answered as per answering guideline.
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