Answer to Question #157588 in Microeconomics for elibariki

Question

1. If the market demand curve is D(p) = 100 − .5p, what is the inverse

demand curve?

2. An addict’s demand function for a drug may be very inelastic, but the

market demand function might be quite elastic. How can this be?

3. If D(p) = 12 − 2p, what price will maximize revenue?

4. Suppose that the demand curve for a good is given by D(p) = 100/p.

What price will maximize revenue?

5. True or false? In a two good model if one good is an inferior good the

other good must be a luxury good

Answer 1

1) Let's find the inverse demand curve:

$$Q(p)-100=-0.5p,$$ $$p=200-2Q(p).$$

2) The changing in price on the drug market could affect on drug's quantity demanded, but the addict always will to pay a higher price for the drug. Therefore, for him the demand function for a drug may be inelastic.

3) By the definition of the total revenue, we have:

$$TR=pq,$$ $$TR=(12-2p)p=12p-2p^2.$$

The total revenue will be maximum, when $\dfrac{dTR}{dP}=0$:

$$12-4p=0,$$ $$p=\dfrac{12}{4}=\$3.$$

4) By the definition of the total revenue, we have:

$$TR=pq,$$ $$TR=(\dfrac{100}{p})p=100.$$

The total revenue will be maximum, when $\dfrac{dTR}{dP}=0$:

$$\dfrac{d}{dP}(100)=0.$$

Therefore, any price will maximize revenue.

5) True.

According to a consumer theory, with two goods, at least one is a normal good. The normal good can be a necessity or a luxury. Then, if one good is inferior, the other must be a luxury.