Answer these questions below one by one, and please use the intermediate microeconomics knowledges to answer it.
Suppose the quantity demanded in the market for coffee can be expressed as
represents the quantity of coffee demanded,
represents the price of coffee,
represents the price of an energy drink, and
represents disposable income.
In the same market, the quantity supplied can be expressed as:
1. Write out a simplified demand function (quantity demanded as a function of the good’s price alone) holding constant the other variables at the following values: and .
2. Using the above equations, find the equilibrium price and quantity in the market. Draw a (fully labeled) supply and demand graph representing this market and its equilibrium.
3. What is the cross-price elasticity between the price of an energy drink () and the quantity of coffee demanded at equilibrium? What does this indicate about the relationship between these two goods?
4. What is the price elasticity of demand at the equilibrium price and quantity? What is the price elasticity of supply at the equilibrium price and quantity?
5. Suppose a new tax of $1 per unit is imposed on coffee, to be collected from sellers. What is the new equilibrium price paid by buyers? What is the new price received by sellers?
6. Who bears a greater burden of the tax, buyers or sellers? Using your answer to (4) above, explain why this makes sense.
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