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Given the demand equation P=-Q* - 4Q +96 (CLO 5) Find Choose
Given the demand equation P=-Q* - 4Q +96 (CLO 5) Find Choose... do/dP Choose... find the price elasticity of demand when P=51 Is the demand inelastic, unit elastic or elastic at these prices Choose... Choose... If this price rises by 2%, calculate the corresponding percentage change in demand.
Given the demand equation P - Q - 4Q +96 (CLO 5) Find Choose... do/dP find the price elasticity of demand when P-51 Is the demand inelastic, unit elastic or elastic at these prices If this price rises by 2%, calculate the corresponding percentage change in demand. Choose... Choose -14 elastic none is correct Inelastic 1/14 -1.469 1 unit elastic -0.75 Next page
Expert Solution
Answer:
P = -Q2 - 4Q + 96
1)From the demand equation,
dP/dQ = -2Q - 4
So, dQ/dP = 1/(dP/dQ)
dQ/dP = 1/(-2Q - 4)
dQ/dP = -1/(2Q+4)
2)The elasticity of demand is given by:
e = (P/Q) * (dQ/dP)
At P = 51,
-Q2 - 4Q + 96 = 51
Q2 + 4Q - 45 = 0
Q = 5 or -9
Since Q cannot be negative, Q = 5
dQ/dP = -1/(2*5 + 4) = -1/14
So, e = (51/5) * (-1/14) = -0.7286
3)Since |e| < 1 at P = 51, the demand is inelastic.
4)% change in price = 2%
Elasticity = e = % change in demand / % change in price
-0.7286 = % change in demand / 2
% change in demand = -1.4572
Thus, the demand decreases by 1.4572%.
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