(Appendix #3) From the original setup in Problem 2, suppose that the quantity su
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Question
(Appendix #3) From the original setup in Problem 2, suppose that the quantity supplied of flat panel TV stands is represented by Q8P 20Pt-200, where P is the price of the stand and Pt is the price of the hardware inputs, and that quantity demanded is QD 4,700 -2P 0.51 $5. where I is income. Assume that at the equilibrium, income is $1,000 and the hardware price is Calculate the income elasticity of demand using calculus. Calculate an input elasticity of supply using calculus. (Hint: Think about cross-price elasticities on the demand side as being analogous to input elasticities on the supply side.) a. b.Explanation / Answer
A.
At equilibrium,
4700-2P +.5I = 8P -20Pi -200
4700-2P+.5*1000 = 8P-20*5 – 200
5200+300 = 10P
P = 550
Q = 4700-2*550+.5*1000 = 4100 units
Again, Demand equation: Q = 4700-2P +.5I ------ (1)
Differentiation of equation 1 w.r.t. I will give dQ/dI.
dQ/dI = .5
Now,
Income elasticity of demand = % change in quantity demanded / % change in income
Income elasticity of demand = (dQ/dI)*(I/Q)
Income elasticity of demand = (.5)*(1000/4100) = .122
B.
Supply equation: Q = 8P – 20Pi - 200 ------ (2)
dQ/dPi = -20
Input elasticity of supply = % change in quantity supplied / % change in price of hardware
Input elasticity of supply = (dQ/dPi)*(Pi/Q)
Input elasticity of supply = (-20)*(5/4100)
Input elasticity of supply = -.024
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