Question

In the estimated model ???̂(??) = 2.25 - 0.7log(??) + 0.02??, where p is the price, q is the quantity demanded of a certain good, and y is disposable income (in thousands of dollars), what is the meaning of the coefficient of log(p)?
a) If the price increases by 1%, the quantity demanded will be 0.007% lower on average, ceteris paribus.
b) If the price increases by 1%, the quantity demanded will be 70% lower on average, ceteris paribus.
c) If the price increases by 1%, the quantity demanded will be 0.7% lower on average, ceteris paribus.
d) None of the answers above is correct.
e) Both (a) and (b) are correct.

Answer 1

Ans. Option c

Estimated model, log(q) = 2.25 - 0.7log(p) + 0.02y

Differentiation of estimated model with respect to price, p,  gives,

1/q * dq/dp = -0.7/p [Because differentiation of log(a) gives 1/a]

=> p/q * dq/dp = -0.7 --> Eq1

The price elasticity of demand = %Change in Quantity Demanded / % change in price = p/q * dq/dp

Thus, Eq1 shows that price elasticity of demand is -0.7.

Therefore, a 1% increase in price level will decrease the quantity demanded by 0.7%

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