Question

Let Q_d be the number of units of a commodity demanded by consumers at a given time t and let Q_sdenote the number of units of the commodity supplied by producers at a given time t. Let p be the price in dollars of the commodity at time t.

Suppose the supply and demand functions for a certain commodity in a competitive market are given, in hundreds of units, by

                                            Q_s = 30 + p + 5 dp/dt

                                             Q_d = 51- 2p + 4 dp/dt

Answer the following questions. Give an explanation for each one:

1. Determine the relationship, if any, between Q_s and Q_d.
2. What does dp/dt signify?
3. At the market equilibrium price, quantity supplied is equal to quantity demanded. Calculate dp/dt at the market equilibrium price.
4. Suppose at time t= 0, the market equilibrium price is 12 Dollars. Express the market equilibrium price as a function of time t.
5. Is there price stability in the marketplace for this item or will the price continue to increase until the economic conditions change?

Answer 1

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