Demand fuction problem

2008-02-18 2:46 am

1.Suppose market price of cereal is $30 per box, and 2000 boxes are sold every week. An economist estimates that the price elasticity of demand for cereal is -1.5 while its elasticity of supply is 0.9.

a)Find the linear demand function and linear supply function of cereal. Show you steps.
b)Due to technological advancements, that supply of cereal rises by 10%. Calculate the impact on the market price of cereal. Show you steps.

thx

回答 (1)

用戶22404

2008-02-18 10:05 pm

✔ 最佳答案

a) Linear demand function:
change in quantity demanded/change in price = -1.5, hence,
(Q-2000)/(P-30) = -1.5
Q-2000=-1.5P+45
1.5P = -Q+2045,
P=-0.67Q+1363.33
Linear supply function:
Change in quantity supplied/change in price = 0.9, thus,
(Q-2000)/(P-30)=0.9
Q-2000=0.9P-27
0.9P=Q-1973
P=1.11Q-2192.22
b) New supply function=>at same price, quantity supplied increased by 10%
P = (1+10%)(1.11Q-2192.22)=1.22Q-2411.44
Solving demand and new supply functions:
-0.67Q+1363.33 = 1.22Q-2411.44
1.891Q=3774.77
Q=1996.18
Hence, P=-0.67(1996.18)+1363.33
P=25.89
Market price decreased from $30 to $25.89 per box

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