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Homework answers / question archive / Assume the market demand for Chicken may be written as Q = 90 - 4p + 0
Assume the market demand for Chicken may be written as Q = 90 - 4p + 0.6Y + 2pb, where Y refers to the income and pb refers to the price of beef. Assuming that chicken and beef both sell for $3, and income is $60, calculate the price elasticity, cross price elasticity and income elasticity for wheat.
Price elasticity
Step one: find Q
Q = 90 - 4p + 0.6Y + 2pb
But
P = $3
Pb = $3
Y = $60
Q = 90 - 4(3) + 0.6(60) + 2(3) = 120 units
Q = 120 units
Step two: find price elasticity
PED = (change in Quantity /change in Price) * (Price / Quantity)
But,
Change in Quantity /change in Price = -4 (obtained by differentiating Q with respect to P in the equation Q = 90 - 4p + 0.6Y + 2pb
Price (P) = 3
Quantity (Q) = 120 units
Hence, PED = (-4) * (3 / 120) = -0.1
PED = -0.1
Cross price elasticity
Cross-price elasticity of demand (XED) = (change in Quantity /change in bp) * (bp / Quantity)
But,
Change in Quantity /change in bp = 2 (obtained by differentiating Q with respect to bp in the equation Q = 90 - 4p + 0.6Y + 2pb
pb = 3
Quantity (Q) = 120 units
Hence, XED = 2 * (3 / 120) = 0.05
Income elasticity (IE)
IE = (change in quantity/change in income) * (income / quantity)
Where;
(Change in quantity/change in income) = 0.6: obtained by differentiating Quantity demanded (Q) with respect to income (Y) in the equation Q = 90 - 4p + 0.6Y + 2pb
Income = $60
Quantity = 120 units
Hence, IE = 0.6 * (60 / 120) = 0.3