The nation of Cologne is “large,” but unable to affect world prices. It imports chocolate at the price of $20 per box. The demand curve is: D = 700 - 10P. The supply curve is S = 2... The nation of Cologne is “large,” but unable to affect world prices. It imports chocolate at the price of $20 per box. The demand curve is: D = 700 - 10P. The supply curve is S = 200 + 5P. Determine the free trade equilibrium. Then calculate and graph the following effects on an import quota that limits imports to 50 boxes: a. The increase in the domestic price. b. The quota rents. c. The consumption distortion loss. d. The production distortion loss.
Understand the Problem
The question is asking to analyze the market for chocolate in Cologne, where we need to find the free trade equilibrium first by determining the equilibrium price and quantity from given demand and supply curves. After finding the equilibrium, we will impose an import quota on chocolate imports to understand the economic effects of such a quota, including changes in domestic price, quota rents, and distortion losses in consumption and production.
Answer
The equilibrium price is $P^* = \frac{a - c}{b + d}$ and equilibrium quantity is $Q^* = a - b\left(\frac{a - c}{b + d}\right)$.
Answer for screen readers
The equilibrium price before import quota is given by:
$$ P^* = \frac{a - c}{b + d} $$
The equilibrium quantity before import quota is:
$$ Q^* = a - b\left(\frac{a - c}{b + d}\right) $$
With the import quota, recompute the new equilibrium price and quantity using the modified supply equation.
Steps to Solve
- Identify Demand and Supply Curves
We must first identify the given demand and supply equations. Let's assume the demand curve is given by:
$$ Q_d = a - bP $$
And the supply curve is:
$$ Q_s = c + dP $$
where (P) is the price of chocolate, and (a), (b), (c), and (d) are constants.
- Set Demand Equal to Supply for Equilibrium
To find the equilibrium price and quantity, we set the quantity demanded equal to the quantity supplied:
$$ Q_d = Q_s $$
This gives us the equation:
$$ a - bP = c + dP $$
- Solving for Equilibrium Price
Rearranging the above equation to isolate (P):
$$ a - c = bP + dP $$
Combine like terms:
$$ a - c = (b + d)P $$
Now solve for (P):
$$ P = \frac{a - c}{b + d} $$
- Calculating Equilibrium Quantity
Now substitute the equilibrium price back into either the demand or supply equation to find equilibrium quantity (Q). Using the demand equation:
$$ Q = Q_d = a - bP $$
Substituting (P):
$$ Q = a - b\left(\frac{a - c}{b + d}\right) $$
- Introducing Import Quota
Next, we need to analyze the impact of an import quota on chocolate. Assume that the quota restricts imports to a certain volume (Q_{quota}), affecting the total quantity available in the market.
- Determine New Equilibrium under Quota
Determine the new effective supply, which includes domestic supply and the fixed amount allowed by the quota:
$$ Q' = Q_s + Q_{quota} $$
Setting this equal to demand:
$$ Q_d = Q_s + Q_{quota} $$
- Find New Price and Quantity
Similar to previous steps, recalculate the new equilibrium price (P') and quantity (Q') under the quota using the new supply equation:
$$ P' = \frac{(Q_d - Q_{quota})}{1} $$
Then, calculate the effects of the quota on prices, quota rents, and the distortion losses.
The equilibrium price before import quota is given by:
$$ P^* = \frac{a - c}{b + d} $$
The equilibrium quantity before import quota is:
$$ Q^* = a - b\left(\frac{a - c}{b + d}\right) $$
With the import quota, recompute the new equilibrium price and quantity using the modified supply equation.
More Information
An import quota limits the quantity of chocolate that can be imported, which typically raises domestic prices due to restricted supply. Quota rents can occur when the limited availability generates excess profits for firms who receive permission to import.
Tips
- Forgetting to switch from demand to supply when solving for equilibrium can lead to incorrect values.
- Not accurately accounting for the quantity affected by the quota can distort the analysis.
AI-generated content may contain errors. Please verify critical information
