1. Connectivity Inc. produces cell phones using labor (L) and machines (K) with the
following production functions, $A(K, L) = 100K + 3K^3 + 22K \times L + 60L - 3L^2$.
Suppose the factory uses two machines and five workers.
a) What are the Marginal Products of Labor and Capital (the numbers)?
b) What is the Average Product of Labor equal (a number)?
c) If Connectivity added one more machine (from two to three), by how many units
would that increase the marginal productivity of labor?
2. The Muffins Factory faces the following cost function for producing muffins:
$C = 72 + 24 \times Ln(Q) + 5Q^2 + \frac{2}{3}Q^3$. Q is the number of muffins. Show all your work.
a) What is its Marginal Cost when it produces 12 muffins?
b) What is the Total Cost equal when it produces four muffins?
c) What is the difference between the Average Variable Cost and Average Fixed Cost
when the Muffin Factory produces eight muffins?
3. Suppose many firms are making identical wireless earbuds. Each company gets $62 per
earbud and has the following profit function: $\Pi = P \times Q - [126 + 14Q + 2Q^2]$
a) How much profit will each company make per earbud?
b) What is the average variable cost at the profit-maximizing quantity?
c) What will happen to this market and the equilibrium price in the long run (explain)
if there are low barriers to entry?
4. Suppose that the wage rate of vineyard workers is $60 per hour. The first worker adds
3 wine bottles to production, the second 4, the third 6, the fourth 8, the fifth 6, the sixth
4, the seventh 3, and the eighth adds 2.
a) Create a table with total production, marginal product, average products, and the
corresponding marginal cost.
b) Draw the Marginal Cost and Marginal Revenue curves based on the information
above on a graph with quantity on the X-axis and cost on the Y-axis.
c) How many workers will this vineyard hire and how many bottles will it produce if
the price of each bottle was $20 and it was a price taker? Show this on the graph and
explain your answer.
