# answers to bonus questions

student

Learning Goal: I’m working on a economics practice test / quiz and need an explanation to help me learn.

We are still helping Catherine to gure out the business strategy of her house-made lunchbox venture (All the analysis is for one day of operation).
Determined by the optimal input decision we solved last time, Catherine’s
business has Total Cost:
C(Q;K) = 50Q2 + rK
which depends on Q number of output – lunch box produced and K units of capital input as x cost.
The capital (kitchen, all the kitchen wares, and raw materials) rents (de- noted by r) for \$20 per hour, labor can be hired for \$30 per hour (wage
denoted by w). Catherine wants to applies her economics knowledge to make the optimal
decision to maximize her pro t.

Bonus 1. Analyzing Catherine’s Pro t Maximization under both Scenarios
a. Compare and discuss the result between Scenario 1 and 2.
b. Plot one graph to each scenario, with the corresponding Demand, MR, MC, ATC, AVC.
c. Indicate the optimal decision, pro t on each graph. If there are areas involved in the graph, please shade them and provide legend properly.
Bonus 2. Indicate the Deadweight Loss (Social Loss) in your graphs above. In
Scenario 2, suppose now government wants to regulate the monopolist Catherine to obtain the social efficiency (only consider social
loss are all generate from monopolistic price manipulation, disregard that Catherine actually uses her intelligent to create her product).
Bonus 3. All the Q1 are for the fi rst day of operation (the x cost happens only on the fi rst day). Does it still make sense if Catherine makes negative
pro t on her first day? What will be the daily pro t for the operation since the second day of operation in each scenarios? At least how
many days will Catherine reach the break-even point in each scenarios for making overall pro t reach back to non-negative)(round up to
the next integer)?

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