Question

In: Accounting

2. The demand function for a truckload of firewood for college students in a small town...

2. The demand function for a truckload of firewood for college students in a small town is Qc = 400 - p. It is sometimes convenient to rewrite a demand function with price on the left side. We refer to such a relationship as the inverse demand function. Therefore, the inverse demand function for college students is p = 400 - Qc. The demand function for other town residents is Qr = 400 - 2p.

• What is the inverse demand function for the other town residents?

• At a price of $300, will college students buy any firewood? What about other town residents? At what price is the quantity demanded by other town residents zero?

• Draw the total demand curve, which sums the demand curves for college students and other residents.

Expert Solution

1. Inverse demand function for the other town residents: Demand function is Qr = 400-2p

or 2p = 400-Qr

or p = 200-0.5Qr

Thus inverse demand function for the other town residents is p = 200-0.5Qr

2. When p is $300 then Qc = 400-p = 400-300 = 100.

Thus at price of $300 college students will buy 100 firewood.

Other town residents will not buy any firewood at this price point as their quantity demanded will be = 400-(2*300) = -200. As demand will not be negative it will be considered as nil.

Let the price at which quantity demanded by other town residents is zero be "x". Thus 0 = 400-2x

or 2x = 400 . Thus x = 200

So, the price at which quantity demanded by other town residents is zero is $200

3. The total demand curve will be based on the demand function for college students and demand function for other residents. The resulting demand curve will be:

In the above chart the x axis represents the quantity demanded and the y axis represents the price

ekkarill92 answered 1 year ago

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