Aggregating Supply and Demand
- V.A.1: Starting from preferences and technologies, solve for partial equilibrium outcomes.
- V.A.2: Know the assumptions underlying perfect competition.
- V.A.4: Calculate the revenue raised and deadweight loss by a commodity tax.
Consider a perfectly competitive market where each consumer’s individual quasilinear demand is given by $q^D = m − p$. $m$ is a measure of how wealthy the consumer is.
Each producer’s supply is given by $q^S = p$.
Suppose that $m=10$ for each consumer, the number of consumers is $N^C = 3$, and the number of producers is $N^P = 10$.
- Algebraically, find the equilibrium quantity and price in this market. Does this match up with what you see in the graphs above?
- What are consumer and producer surplus?
Now, increase the number of consumers, $N^C$, from 3 to 4. Answer parts (c) and (d) qualititatively with the graph and then quantitatively using algebra.
- What happens to the equilibrium quantity and price?
- How does this change affect the welfare of the producers and the original consumers?
Bring the $N^C$ and $N^F$ back to their original values, and increase the “wealth” of each consumer from $m=10$ to $m=11$. Answer parts (e) and (f) qualititatively with the graph and then quantitatively using algebra.
- What happens to the equilibrium quantity and price?
- How does this change affect the welfare of the producers and consumers?
Bring $m$ back to its original value and increase the number of producers from $N^P=10$ to $N^P=11$. Answer parts (g) and (h) qualititatively with the graph and then quantitatively using algebra.
- What happens to the equilibrium quantity and price?
- How does this change affect the welfare of the consumers and the original producers?