Optimal Inputs & Demand for Labor: Small Business Profit Maximization

Smaller firms in large competitive markets are typically $$price$-$takers$$ which must sell products at the market$$s

equilibrium retail price $($or less$)$ and also must accept the market$$s standard costs for the two types of inputs: capital

and labor. While these firms have limited $$market power$$ in both input and output pricing, they are still able choose

the most efficient combination of input quantities to maximize profits. Assume market demand is sufficient for firms

to sell any profit$-$maximizing quantity that they can produce $($within the constraint of its production function$)$ at the

market retail price. Open the Excel Spreadsheet $($on Canvas$)$ showing an example small firm$$s detailed internal

microeconomic characteristics with formulas pre$-$populated to demonstrate how different variables and outcomes

are likely to vary with this firm$$s choices of capital and labor $($the two inputs for a standard production function$).$

Only make changes to cells A$2,$ B$2,$ D$2,$ L$2$ : The sheet will update from these.

Enter the given values for the following scenarios to quantify this firm$$s demand for labor $($how many workers it

wants to hire$)$ and its total profit under optimal management for each of the following separate scenarios:

a$.$ $$11$ wage and $6$ machines with a $$27$ retail price and $$1000$ fixed cost

b$.$ $$14$ wage and $6$ machines with a $$27$ retail price and $$1000$ fixed cost

c$.$ $$14$ wage and $6$ machines with a $$35$ retail price and $$1000$ fixed cost

d$.$ $$20$ wage and $6$ machines with a $$50$ retail price and $$1000$ fixed cost

e$.$ $$20$ wage and $5$ machines with a $$50$ retail price and $$1000$ fixed cost

f$.$ $$20$ wage and $5$ machines with a $$50$ retail price and $$1500$ fixed cost $($higher property taxes or rent$)$