Question

1. Consider the following monopolistic market:

Demand:     P = 30 – 0.5Q

Costs:         TC = 100+Q²

1. Solve for the monopoly’s optimal price and quantity.   How much is the profit?
2. Please calculate elasticity of demand. And verify the mark-up formula.   
3. Now consider a unit tax of $5/unit to be paid by the seller. Draw the market demand and marginal cost curves before and after the tax. Solve for the new consumer and producer prices and the market quantity with the tax.
4. Based on your calculation, how much is the tax revenue? How much of it are paid by the consumers and how much by the producers?

2. Consider the following perfectly competitive market:

Demand:     P = 30 – 0.5Q

Supply:        P = 2Q

1. Solve for the market price and quantity without any government intervention.
2. Now consider a unit tax of $5/unit to be paid by the seller. Draw the market demand and supply before and after the tax. Solve for the new consumer and producer prices and the market quantity with the tax.
3. Based on your calculation, how much is the tax revenue? How much of it are paid by the consumers and how much by the producers?

Answer 1