Question

Suppose Ernie is opening a new restaurant that will produce pizzas using a combination of workers (LL) and ovens (KK). Ernie knows from experience that the total number of pizzas he can produce in an hour is given by the function q=3K0.5L0.5q=3K0.5L0.5. Ernie can rent ovens for an hourly cost of $4 and must pay his employees $9 per hour.

Therefore, his total hourly cost function is given by TC =   .

Complete the following table by calculating the total cost of producing 9 pizzas per hour using 2 and 4 workers.

Pizzas per Hour	Workers	Ovens	Total Cost (TC)
(q)	(L)	(K)	(Dollars)
9	1	9
9	2	4.50	36.00
9	3	3.00
9	4	2.25	45.00

The cost-minimizing bundle of labor and capital used to produce 9 pizzas is   .

Based on this, the optimal combination for the given wage and rental rate of capital, the rate of technical substitution of labor for capital, when producing optimally, is   .

Suppose Ernie wants to double the number of pizzas he makes in an hour.

Complete the following table by computing the total cost associated with each of the following input combinations.

Pizzas per Hour	Workers	Ovens	Total Cost
(q)	(L)	(K)	(Dollars)
18	2	18.00
18	3	12.00	75.00
18	4	9.00
18	5	7.20	73.80

At the new level of output, the optimal combination of labor and capital is   . The cost-minimizing ratio of labor to capital to produce 18 is   the cost-minimizing ratio needed to produce 9 pizzas. This is always true of production functions that exhibit   returns to scale.

On the following graph, use the blue line (circle symbols) to show the long-run total cost function by plotting the minimum total costs associated with producing 9 and 18 pizzas, based on your answers to the previous questions.

Answer 1