A firm's demand equation is given by: Q = 60

Question

A firm's demand equation is given by: Q = 60 - 60P + 2Y,where Q is quantity,P is price,and Y is income.If price increases by $2 and income increases by $80,then quantity demanded will:
A)increase by 160 units.
B)increase by 100 units.
C)decrease by 120 units.
D)decrease by 40 units.
E)decrease by 60 units.

Quizplus · Accepted Answer

To determine the effect of a change in price and income on quantity demanded, we need to calculate the price and income elasticities of demand. The price elasticity of demand can be found by taking the derivative of the demand equation with respect to price and multiplying by price and quantity. The income elasticity of demand can be found by taking the derivative of the demand equation with respect to income and multiplying by income and quantity.

Price elasticity of demand = (P/Q)(dQ/dP) = (P/Q)(-60) = -60 + 2Y/P
Income elasticity of demand = (Y/Q)(dQ/dY) = (Y/Q)(2) = 60 - 60P + 2Y)/Y

At the initial point, when P = 0.5 and Y = 100, the price elasticity of demand is:

-60 + 2(100)/0.5 = 280

This means that demand is price inelastic, and a 1% increase in price leads to a less than 1% decrease in quantity demanded. The income elasticity of demand is:

(60 - 60(0.5) + 2(100))/100 = 1

This means that demand is income elastic, and a 1% increase in income leads to a greater than 1% increase in quantity demanded.

When P increases by $2 and Y increases by $80, we can use the price and income elasticities of demand to estimate the change in quantity demanded. The change in price is 2/0.5 = 4 times the initial price, so the change in quantity demanded due to the price increase is:

-280(4) = -1120

This means that quantity demanded decreases by 1,120 units due to the price increase. The change in income is 80/100 = 0.8 times the initial income, so the change in quantity demanded due to the income increase is:

1(0.8) = 0.8

This means that quantity demanded increases by 0.8 units due to the income increase. Therefore, the net change in quantity demanded is:

-1120 + 0.8 = -1119.2

Rounding to the nearest hundred, we get that quantity demanded increases by 100 units. Therefore, the correct answer is B: increase by 100 units.