I would like to have the following sample problems solved in EXCEL format so that I can see the formula used.
1. TC = 17 + 2q2
Suppose the firm's output can be sold (in integer units) at $57 per unit.
Using calculus and formulas (but no tables or spreadsheets) to find a solution, HOW MANY UNITS should the firm produce to maximize profit?
2. Assume that a monopolist faces a demand curve for its product given by:
p = 80 - 2q
Further assume that the firm's cost function is:
TC = 560 + 13q
Using calculus and formulas (but no tables or spreadsheets) to find a solution, WHAT IS THE PROFIT (rounded to the nearest integer) for the firm at the optimal price and quantity?
Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should then round to the nearest cent. Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items.
Hint: Define a formula for Total Revenue using the demand curve equation. Then take the derivative of the Total Revenue and Total Cost formulas. Use these derivative equations to perform a marginal analysis.
The problem set deals with finding the quantity from demand equation and maximum revenue.