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?
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?
