Calculation on Price Elasticity of Demand problem .... Need Advices .....

DreamBell

Give following demand function:

Q = 2.0 P^-1.33Y^2.0A^0.50

Q = Quantity demanded (Thousads of units)
P = Prices ($/Unit)
Y = Disposable income per capita ($ thousands)
A = Advertising expenditures ($ thousands)

When P = $2/unit, Y = $8 (i.e. $8000), and A = $25 (i.e. $25000)...

1. Price Elasticity of demand
2. The approximate percentage increase in demand if disposable income percentage increased by 3%.
3. The approximate percentage increase in demand if Advertising Expenditure are increased by 5%.

Well, i really not so understand how to resolved the ab0ve question. Is that i need to draft a graft in order to get the answer ???

Hopefully hav some one professional here to guide me on this kind of question .

regards,
Dream Bell

Borek

I have no idea about the economy part of the question, but you will not probably get much help, as your post is ambiguous and not clear. I can only guess that equation for Q is given, and points 1-3 are things that you are expected to calculate.

If so, 2 & 3 looks like simple plug and chug.

John Creighto

For (1) use the definition of price elasticity. This should involve a partial derivative. For 2 and 3 formula use the definition of percent change. (Y2-y1)/Y1*100%. Less formula (for example in 2) you could simply replace Y by 1.03Y and see how this effects Q.

talk2glenn

This is almost identical to your previous question, but the derivative is just a little more complicated. Still uses the same rule, though.

For number 1, the equation for price elasticity of demand is Ep(Q) = Q'(P) * P/Q.

Try to solve for Q'(P) on your own using the formula I gave you in your other post (given Ax^B, d(x) = A*B*x^B-1, and you get to hold Y and A constant when taking derivative with respect to P).

From there, you just plug price in for P, and solve for Q given the values in the problem, which you plug into the denominator, and multiply by the derivative with respect to P. This will give you a number between 0 and infinity (typically between 0 and 2), which is the price elasticity of demand.

For number 2, you first need to find the income elasticity of demand. This is Ey(Q) = Q'(Y) * Y/Q, and is found the exact same way as price elasticity, just w.r.t. a different variable. Multiply the result by 3 to get the percent change in demand that follows a 3% change in income.

For number 3, you are finding the advertising elasticity of demand. This is Ea(Q) = Q'(A) * A/Q. See the trend here? Multiply that result by 5 to get the change after a 5% change in advertising expenditures. I'm sorry if this isn't very clear, but hopefully it helps.

Good luck.

John Creighto

Ah, I missed the word approximate.