Answer to Question #249983 in Microeconomics for Mohnish Rathore

Question

statistics department of an appliance manufacturer has estimated that

demand function (number purchased annually) for their (Brand X) automatic

washer is as follows:

Qx=197,000-100P+50Py+0.0251 +0.02A + 10,000P

where

ex- quantity purchased,

Px price of the company's washer,

Py = price of a major competitor's washer,

I= average household income,

A= annual dollars spent on advertising

PL = cost of doing one load of wash in self-service laundry.

a. If Py=$300, I=$40,000, A-$200,000, and P =$.30, find the price elasticity of demand between Py=$350 and P$400. (When P = $400, with the values of the other variables as given above, then Qx = 180,000.)

b. Is EpX elastic, inelastic, or unitary elastic? Why? If the price is cut, does total revenue increase, decrease, or not change?

c. Find the income elasticity of demand for Qy, given Py=$400. The other vari ables are as given in part (a). Interpret your answer-that is, what does it say, if anything, about the demand for Brand X washers?

Answer 1

$Q_x=197000-100P+50P_y+0.025I+0.02A+10000P$

$=197000-100(400)+50(300)+0.025(40000)+0.02(200000)+10000(30)$

$=207000$

Percentage change in quantity:

$= \frac{207000-180000}{207000}\times100=13$ %

Percentage change in price:

$=\frac{300-350}{300}\times100=-16.7$ %

Price Elasticity of demand:

$=\frac{13}{-16.7}=-0.8.$

(b)

Demand is elastic. The negative sign implies that price and the quantity demanded are inversely related.

If price is cut, the total revenue will increase because more quantity will be demanded at the lower price.