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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.  

a. Assuming that your firm’s demand function is linear (i.e., Q(P)=a-bP). Estimate your demand function.

b. You have fixed costs of $7,800 per week and variable costs of $10 per t-shirt. What is your firm’s cost function?

c. What is your firm’s profit function?

d. Calculate the profit maximizing quantity, Q*, that your firm should produce

e. Calculate the profit maximizing price that your firm should charge

f. Calculate profits at the profit-maximizing price

g. 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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