Question

A monopolist faces an inverse demand given by $P = 1020 - 10Q$ where $P$ is the price of of the good they sell and $Q$ represents the quantity produced and sold at the market price $P$. The monopolist's cost function is given by $C(Q) = 10,000 + 20Q$ where $Q$ is the quantity produced and $C$ represents the cost in dollars. a) [30P] Find the optimal price and quantity that the monopolist would choose under the assumption that their goal is to maximize profits. Show all of the steps required to arrive at the solution.¹ b) [20P] Compute the profits of this monopolist. Show all of the steps required to arrive at the solution. c) [30P] In a diagram with the market demand, identify the deadweight loss (DWL) arising from this monopoly (DWL shape depends on demand and cost functions so make sure your sketch resemble the shapes of the particular cost and demand functions in this problem) and then compute this amount. Hint: the size of a DWL is typically the area of some \"triangle\". Area of a triangle is just base*height. See sections 9.3 and 9.4 in the textbook. d) [20P] Now assume that the government imposes a tax/unit of $100. Find (and show all of the steps required) the optimal price and quantity in the presence of this tax. Does the monopolist pass the whole tax to consumers? Hint: compare the prices consumers would pay without a tax, versus the new price the monopolist charges if there is a tax.

          A monopolist faces an inverse demand given by $P = 1020 - 10Q$ where $P$ is the price of of the good they sell and $Q$ represents the quantity produced and sold at the market price $P$. The monopolist's cost function is given by $C(Q) = 10,000 + 20Q$ where $Q$ is the quantity produced and $C$ represents the cost in dollars.
a) [30P] Find the optimal price and quantity that the monopolist would choose under the assumption that their goal is to maximize profits. Show all of the steps required to arrive at the solution.¹
b) [20P] Compute the profits of this monopolist. Show all of the steps required to arrive at the solution.
c) [30P] In a diagram with the market demand, identify the deadweight loss (DWL) arising from this monopoly (DWL shape depends on demand and cost functions so make sure your sketch resemble the shapes of the particular cost and demand functions in this problem) and then compute this amount. Hint: the size of a DWL is typically the area of some \"triangle\". Area of a triangle is just base*height. See sections 9.3 and 9.4 in the textbook.
d) [20P] Now assume that the government imposes a tax/unit of $100. Find (and show all of the steps required) the optimal price and quantity in the presence of this tax. Does the monopolist pass the whole tax to consumers? Hint: compare the prices consumers would pay without a tax, versus the new price the monopolist charges if there is a tax.

A monopolist faces an inverse demand given by P = 1020 - 10Q where P is the price of of the good they sell and Q represents the quantity produced and sold at the market price P. The monopolist's cost function is given by C(Q) = 10,000 + 20Q where Q is the quantity produced and C represents the cost in dollars.
a) [30P] Find the optimal price and quantity that the monopolist would choose under the assumption that their goal is to maximize profits. Show all of the steps required to arrive at the solution.¹
b) [20P] Compute the profits of this monopolist. Show all of the steps required to arrive at the solution.
c) [30P] In a diagram with the market demand, identify the deadweight loss (DWL) arising from this monopoly (DWL shape depends on demand and cost functions so make sure your sketch resemble the shapes of the particular cost and demand functions in this problem) and then compute this amount. Hint: the size of a DWL is typically the area of some ẗriangle.̈ Area of a triangle is just base*height. See sections 9.3 and 9.4 in the textbook.
d) [20P] Now assume that the government imposes a tax/unit of 100. Find (and show all of the steps required) the optimal price and quantity in the presence of this tax. Does the monopolist pass the whole tax to consumers? Hint: compare the prices consumers would pay without a tax, versus the new price the monopolist charges if there is a tax.

Added by Steven B.

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