Economics 4320 Intermediate
Problems
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(Demand Estimation and Profit Maximization).
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(3 points) Assuming that your firm’s demand function is linear (i.e., ), estimate your demand function.
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(3 points) You have fixed costs of $7,800 per week and variable costs of $10 per t-shirt. What is your firm’s cost function?
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(3 points) What is your firm’s profit function?
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(3 points) Calculate the profit maximizing quantity, , that your firm should produce
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(3 points) Calculate the profit maximizing price that your firm should charge
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(3 points) Calculate profits at the profit maximizing price
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(3 points) Calculate profits at your original price of $22. Is this higher or lower than profits at the profit maximizing price? Is this what you would expect?
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2.(18 points) Profit Maximization
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3.(18 points) Profit Maximization
See Lectures 3 and 16
You run a firm that sells custom t-shirts over the Internet. You want to work out the price you should charge to maximize profits. To do this, you decide to run a market experiment. You lower your price from your standard price of $22 to $20.
When you do this, your weekly sales increase from 4,400 t-shirts per week to 4,800 t-shirts per week.
Your firm faces the following demand curve:
Your firm’s cost function is:
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A.(3 points) Calculate the price elasticity of demand (as a function of price)
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B.(3 points) Calculate the profit function
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C.(3 points) Calculate the profit maximizing quantity Q*
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D.(3 points) Calculate the profit maximizing price P*
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E.(3 points) Calculate profits at the profit maximizing price and quantity
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F.(3 points) Calculate the markup on price at the profit maximizing price
Note:
Hint: Calculate the marginal cost by taking the derivative of the cost function
Your firm faces the following demand curve:
Your firm’s cost function is:
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A.(3 points) Calculate the price elasticity of demand (as a function of price)
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B.(3 points) Calculate the profit function
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C.(3 points) Calculate the profit maximizing quantity Q*
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D.(3 points) Calculate the profit maximizing price P*
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E.(3 points) Calculate profits at the profit maximizing price and quantity
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F.(3 points) Calculate the markup on price at the profit maximizing
Note:
Hint: Calculate the marginal cost by taking the derivative of the cost function
DETAILED ASSIGNMENT