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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

Economics

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.

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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