Question

a) Given the following nonlinear function of pork Q=1000-P²+lnP_B+lnY², where Q is the quantity demanded for pork, P_B is the price beef and Y is the consumer's income. If P=N$10,P_B=N$100 and Y=N$5, calculate the following elasticities and interpret the results.

i) Price elasticity of demand

ii) Cross price elasticity of demand between pork and beef

iii) Income elasticity of demand

b) Is it true, as many people claim, that taxes assessed on producers are passed along to consumer? That is, do consumers pay for entire tax?

Answer 1

Solution :

Q = 1000 - P² + lnPB + lnY²
Q = 1000 - (10)2 + ln(100) + ln(5)²
Q = 1000 - 100 + 4.61 +3.22
Q = 907.83

i) Price elasticity of demand = (dQ/dP)*(P/Q)
= (-2)*(10/907.83)*10
= -0.22

ii) Cross price elasticity of demand = (dQ/dP_B)*(P_B/Q)
= (1/P_B)*(P_B/907.83)
= 0.001

iii) Income elasticity of demand = (dQ/dY)*(Y/Q)
= (2/Y)*(Y/Q)
= 2/907.83
= 0.002

B):- Yes, it is true because if the producers will not do so then they supplied will be reduced because the costs of inputs including tax will increase..

Consumers pay for the entire tax depends on the elasticity of demand of the goods.

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