Market Equilibrium: Tax vs Production Quota for Crystal Production

a) What is the market clearing price and quantity of crystals without any tax or quota?

Calculate the market equilibrium price and quantity when there is no tax or production quota.

b) Would a crystal-producing business owner prefer the proposed tax or quota system? Why?

Discuss the preferences of a crystal-producing business owner between the tax and production quota systems.

a) Market Clearing Price and Quantity Without Tax or Quota

The market clearing price is $5 per pound, and the quantity is 5 million pounds without any tax or quota.

b) Preference of a Crystal Producer for Tax System

A crystal producer would prefer the proposed tax system over the production quota. Find out why in the detailed explanation below.

In a market without any tax or production quota, the equilibrium price of crystals is determined where the aggregate demand equals the aggregate supply. The given equations for aggregate demand (Q=10-P) and aggregate supply (Q=P) can be set equal to find the equilibrium price and quantity.

Setting Q=10-P equal to Q=P, we get 10-P=P which simplifies to P=10/2=5. Substituting the price back into either equation gives the equilibrium quantity of Q=10-5=5 million pounds.

Now, when considering the preference of a crystal producer such as Walt, the impact of the proposed tax and production quota on the market equilibrium must be evaluated. With a tax of $4 per pound, the market price would increase to $9 per pound, and the quantity demanded would decrease to 6 million pounds. This change in equilibrium would lead to higher prices but lower production levels.

For Walt, the crystal producer, choosing the tax system would allow him to continue production and sales. Despite paying the tax per pound, the higher market price would compensate for this cost, potentially leading to increased revenue and profits. On the other hand, a production quota of 3 million pounds would restrict Walt's ability to meet market demand, limiting his revenue and profits.

Therefore, Walt would likely prefer the tax system as it enables him to continue business operations and benefit from higher prices. This preference is based on the understanding that the tax can be passed on to consumers through higher prices, while a production quota would directly limit his output and revenue potential.

In summary, the market clearing price and quantity of crystals without any tax or quota are $5 per pound and 5 million pounds, respectively. A crystal producer like Walt would prefer the proposed tax system over a production quota due to its potential for higher revenue and profits in the market.