The demand for haddock has been estimated as log Q = a=b log p=cl log I = d log
ID: 1242501 • Letter: T
Question
The demand for haddock has been estimated as log Q = a=b log p=cl log I = d log Pm Where Q= quantity of haddock sold in New England P = price per pound of haddock I =a measure of personal income in the New England region and Pm= an index of the price of meat and poultry. If b= -2.174, c= 0.461, and d= 1.909. a) Determine the price elasticity of demand . b) Detrmine the income elasticity of demand. c) Determine the cross elasticity of demand. d) How would you charaterize the demand for haddock? e) suppose disposable income is expected to increase by 5 percent next year. Assuming all other factors remain constant, forecast the percentage change in the quantity of haddock demanded next year.Explanation / Answer
log Q = a x log e + 2.174 log P + 0.0461 x Log I + 1.909 x log Pm [Since log e = 1]
log Q = log ea + log P2.174 + log I0.0461 + log Pm1.909
log Q = log (ea x P2.174 x I0.0461 x Pm1.909)
Q = (ea x P2.174 x I0.0461 x Pm1.909)
(a) Price elasticity of demand = (dQ / dP) x (P / Q)
= 2.174 x (ea x P1.174 x I0.0461 x Pm1.909) x (P / Q)
= 2.174 x (ea x P2.174 x I0.0461 x Pm1.909) / Q
= 2.174 x (Q / Q) = 2.174
(b) Income elasticity of demand = (dQ / dI) x (I / Q)
= 0.0461 x (ea x P1.174 x I - 0.9539 x Pm1.909) x (I / Q)
= 0.0461 x (ea x P1.174 x I0.0461 x Pm1.909) / Q
= 0.0461 x (Q / Q)
= 0.0461
(c) Cross price elasticity = (dQ / dPm) x (Pm / Q)
= 1.909 x ((ea x P1.174 x I0.0461 x Pm0.909) x (P / Q)
= 1.909 x (ea x P1.174 x I0.0461 x Pm1.909) / Q
= 1.909 x (Q / Q)
= 1.909
(d) The demand function is independent of values of P, I and Pm.
(e) Sinc income elasticity is 0.0461, it means that if income increases by 1%, Q increases by 0.0461%.
So, when income increases by 5%, Q increases by (0.461 x 5) = 0.2305%.
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