Problem set 1 — Equilibrium and welfare

Show your working. Quantities and prices follow the course convention: inverse demand $p = a - bq$, inverse supply $p = c + dq$.

Problem 1 — Warm-up

Let $a = 90$, $b = 1$, $c = 10$, $d = 1$.

1. Find $q^*$ and $p^*$.
2. Compute $CS$, $PS$, and $TS$.
3. Verify $TS = \tfrac{1}{2}(a - c)\,q^*$ without using your answer to part 2.

Problem 2 — A binding price ceiling

Let $a = 80$, $b = 0.8$, $c = 20$, $d = 1.2$, and impose a price ceiling $\bar{p} = 44$.

1. Confirm the ceiling binds and find the quantity traded $q_t$.
2. Compute the excess demand at $\bar{p}$.
3. Compute $CS$, $PS$, and the deadweight loss. (Careful: with a binding ceiling the consumer-surplus region is a trapezoid, not a triangle.)
4. Check your answers against Tool 3.

Answers will be discussed in class.