Suppose there are two types of food: Slow and Fast. Slow food is food that takes a lot of time and energy to prepare, and is possibly more “authentic.” Consider it a high-end luxury good. All other food we’ll call Fast. It’s a staple needed to live, is quick to acquire and cheap. The slow food costs $20 per unit, while the fast food costs $5 per unit. The price elasticity of demand for slow food is -2.8. The price elasticity of demand for fast food is -.20. The government is considering a tax on food. The tax on slow food is denoted ts, and the tax on fast food is denoted tf.
a. Comment on the significance of the different elasticities of demand?
b. What is the equation for the optimal (Ramsey) value of ts in terms of tf.
c. In a clearly written paragraph, comment on the relative size of ts compared to tf, and why we are seeing this result.
d. Suppose the government has selected tax levels ts and tf using the Ramsey rule. Furthermore, at those taxes, the market sells 3 million units of slow food and 300 million units of fast food., the government collects $1 billion in revenue from these taxes. What are the values of th and tp?
Answer:
The different price elasticities of the two goods help in explaining the behavior of the two goods in the market. That is the responses of the quantity demanded with change in prices. Slow food shows that 1% change in price results to decline in quantity demanded by 2.8 units while fast foods shows that 1% change in price will results to decline in quantity by 2 units.
Optimal value of fast food VF= $5 – t f
Optimal value for slow food VS=$20 – t s
The t s in fast moving foods is low because of the low price elasticity of demand of -2.0 while the t f in slow food is high due to high price elasticity of demand of -2.8.
300 units of fast foods
3 million units of slow foods
Rev 1 billion, therefore TS= 3/303 *1Billion=9900990
T f=300/303 * 1Billion=990099010
a. Comment on the significance of the different elasticities of demand?
b. What is the equation for the optimal (Ramsey) value of ts in terms of tf.
c. In a clearly written paragraph, comment on the relative size of ts compared to tf, and why we are seeing this result.
d. Suppose the government has selected tax levels ts and tf using the Ramsey rule. Furthermore, at those taxes, the market sells 3 million units of slow food and 300 million units of fast food., the government collects $1 billion in revenue from these taxes. What are the values of th and tp?
Answer:
The different price elasticities of the two goods help in explaining the behavior of the two goods in the market. That is the responses of the quantity demanded with change in prices. Slow food shows that 1% change in price results to decline in quantity demanded by 2.8 units while fast foods shows that 1% change in price will results to decline in quantity by 2 units.
Optimal value of fast food VF= $5 – t f
Optimal value for slow food VS=$20 – t s
The t s in fast moving foods is low because of the low price elasticity of demand of -2.0 while the t f in slow food is high due to high price elasticity of demand of -2.8.
300 units of fast foods
3 million units of slow foods
Rev 1 billion, therefore TS= 3/303 *1Billion=9900990
T f=300/303 * 1Billion=990099010
