Economics Homework Help. Need answers to bonus questions
Catherine plan to start a house-made lunchbox business that sells healthy
lunchbox during the COVID pandemic. The business has a production
function
Q = 10K0:3L0:7
where K denotes the unit of capital inputs per hour and L denotes the
unit of labor inputs per hour used in producing Q number of lunch box.
The capital (kitchen, all the kitchen wares, and raw materials) rents for
$20 per hour, labor can be hired for $30 per hour.
Catherine wants to applies her economics knowledge to make the optimal
decision to minimize the cost of the production.
Bonus 1. Solve the Q1c and Q1d by using Lagrangian
a. Write down the Cost Minimization Problem.
b. Write down the corresponding Lagrangian.
c. Find the optimal capital-labor ratio.
d. Given $10,000 budget find the exact optimal amount of labor
input, capital input and total output level.
Bonus 2. Fill the rest of the blanks in Q1c. And draw a sketch of AC, AFC and
AVC in the same graph (no need to be extremely precise, just with
the numbers calculated from the table and the correct curvature).
