Question

Suppose P = 500 − 0.01Q − 0.02√Q is the demand equation for a product. Find the rate of change of quantity with respect to price.​

Answer 1

Answer:

Consumer and Producer Surplus

Here are a demand and a supply curve for a product. Which is which?

graph

The demand curve is decreasing – lower prices are associated with higher quantities demanded, higher prices are associated with lower quantities demanded. Demand curves are often shown as if they were linear, but there’s no reason they have to be.

The supply curve is increasing – lower prices are associated with lower supply, and higher prices are associated with higher quantities supplied.

The point where the demand and supply curve cross is called the equilibrium point (q∗,p∗)(q∗,p∗).

graph

Consumer and Producer Surplus

Given a demand function p=d(q)p=d(q) and a supply function p=s(q)p=s(q), and the equilibrium point (q∗,p∗)(q∗,p∗)

The consumer surplus is

∫0q∗d(q)dq−p∗q∗.

∫0q∗d(q)dq−p∗q∗.

The producer surplus is

p∗q∗−∫0q∗s(q)dq.

p∗q∗−∫0q∗s(q)dq.

The sum of the consumer surplus and producer surplus is the total gains from trade.

Explanation:

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