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The problem you provided involves supply and demand curves for coffee, with specific questions about equilibrium price and quantity, consumer surplus, producer surplus, and the effects of price ceilings and floors. Let's break it down step-by-step.

### Given:
- Demand curve: $ Q_d = 1200 - 3P $
- Supply curve: $ Q_s = -300 + 2P $

### (a) Compute the market equilibrium price and quantity.
At equilibrium, quantity demanded equals quantity supplied, $ Q_d = Q_s $.

So, set the two equations equal to each other:

\[
1200 - 3P = -300 + 2P
\]

Solving for $ P $:

\[
1200 + 300 = 2P + 3P
\]
\[
1500 = 5P
\]
\[
P = 300
\]

Now substitute $ P = 300 $ into either the demand or supply equation to find the equilibrium quantity:

\[
Q_d = 1200 - 3(300) = 1200 - 900 = 300
\]

So, the equilibrium price is **$300** and the equilibrium quantity is **300 units**.

### (b) Calculate the consumer surplus, the producer surplus, and the total surplus at equilibrium.

#### Consumer Surplus (CS):
Consumer surplus is the area of the triangle under the demand curve but above the equilibrium price. The formula for consumer surplus is:

\[
CS = \frac{1}{2} \times \text{base} \times \text{height}
\]

The base is the equilibrium quantity (300 units), and the height is the difference between the maximum price consumers are willing to pay (intercept of the demand curve, when $ Q_d = 0 $) and the equilibrium price.

From the demand curve $ Q_d = 1200 - 3P $, when $ Q_d = 0 $:

\[
0 = 1200 - 3P \implies P = 400
\]

So, the maximum price consumers are willing to pay is $400. The height is $ 400 - 300 = 100 $.

Thus, the consumer surplus is:

\[
CS = \frac{1}{2} \times 300 \times 100 = 15000
\]

#### Producer Surplus (PS):
Producer surplus is the area of the triangle above the supply curve but below the equilibrium price. The formula for producer surplus is:

\[
PS = \frac{1}{2} \times \text{base} \times \text{height}
\]

The base is again the equilibrium quantity (300 units), and the height is the difference between the equilibrium price and the minimum price producers are willing to accept (intercept of the supply curve, when $ Q_s = 0 $).

From the supply curve $ Q_s = -300 + 2P $, when $ Q_s = 0 $:

\[
0 = -300 + 2P \implies P = 150
\]

So, the minimum price producers are willing to accept is $150. The height is $ 300 - 150 = 150 $.

Thus, the producer surplus is:

\[
PS = \frac{1}{2} \times 300 \times 150 = 22500
\]

#### Total Surplus (TS):
Total surplus is the sum of consumer surplus and producer surplus:

\[
TS = CS + PS = 15000 + 22500 = 37500
\]

---

Let me know if you'd like to continue with the next parts or have any questions about this! Here are some related questions to consider:

1. How would the equilibrium change if the demand curve shifted to the right?
2. What happens to consumer surplus if the price ceiling is set below the equilibrium price?
3. How does a price floor above the equilibrium price affect producer surplus?
4. What are the welfare implications of a price ceiling or price floor in a market?
5. Can total surplus ever increase with a price ceiling or floor?

**Tip:** Price ceilings and floors often lead to inefficiencies like shortages and surpluses, which can reduce the total surplus in the market.

The demand and the supply curves for coffee are given by Q_d = 1200 - 3P and Q_s = -300 + 2P. (a) Compute the market equilibrium price and quantity. (b) Calculate the consumer surplus, the producer surplus, and the total surplus at the equilibrium. (c) Suppose a price ceiling of $250 is set. i. Will there be a shortage or a surplus in the market? If so, how much? ii. What is the change in consumer surplus caused by the price ceiling? iii. What is the change in producer surplus caused by the price ceiling? iv. What is the total surplus after imposing the price ceiling? (d) Suppose a price floor of $250 is set. i. Will there be a shortage or a surplus in the market? If so, how much? ii. What is the change in consumer surplus caused by the price floor? iii. What is the change in producer surplus caused by the price floor? iv. What is the total surplus after imposing the price floor? (e) In which case is total surplus maximized (i.e. with the price ceiling, the price floor or with neither)? Explain.

This problem involves calculating market equilibrium price and quantity, consumer and producer surplus, and analyzing the effects of price ceilings and price floors. It provides a comprehensive approach to understanding the impact of government-imposed price controls on total surplus.

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