You sell electric bikes in a small town. As shop owner and operator, you have observed that your weekly sales tend to follow a pattern that can be stated as:

Q = 310 - .25PP + 1.25A + .1PR + 2Y

where Q = unit sales of bikes, PP = price of bikes, A = advertising expenses (in thousands of dollars), PR = price of a rival's bikes, Y = per capita income of customers in thousands of dollars. You are currently charging $1600 for your bikes and spending $200,000 in advertising, and per capita income is $60,000. Your rival is charging $1500 for their bikes.

1. Calculate your predicted quantity of bikes sold given these values. Show the reduced demand function (keeping own price as the only variable on the right-hand side).
2. Compute point elasticities for own price, advertising, cross-price, and income. Using advertising elasticity, if your advertising level rises by 5%, by what percent (approximately) will sales increase?
3. Draw a general demand curve for your bikes (no intercept calculation needed). Now predict what happens to your quantity sold if your rival drops price to $1300 but income rises to $80,000, and show the demand change.
4. Refer back to the initial values for all the variables, with your current price of $1600. If you are maximizing revenue, should you increase or decrease price? Calculate the revenue-maximizing price.