Suppose Paolo is opening a new restaurant that will produce pizzas using a combination of workers (LL) and ovens (KK). Paolo knows from experience that the total number of pizzas he can produce in an hour is given by the function q=10K0.5L0.5q=10K0.5L0.5. Paolo can rent ovens for an hourly cost of $10 and must pay his employees $10 per hour.

Therefore, his total hourly cost function is given by .

Complete the following table by calculating the total cost of producing 20 pizzas per hour using 1 and 3 workers.

Pizzas per Hour	Workers	Ovens	Total Cost
(q)	(L)	(K)	(Dollars)
20	1	4
20	2	2	40.00
20	3	1.33
20	4	1	50.00

The cost-minimizing bundle of labor and capital used to produce 20 pizzas is .

In this example, the rate of technical substitution of labor for capital, when producing optimally, is .

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

Complete the following table by computing the total cost of producing 20 pizzas per hour using 3 and 4 workers.

Pizzas per Hour	Workers	Ovens	Total Cost
(q)	(L)	(K)	(Dollars)
40	2	8
40	3	5.33	83.30
40	4	4
40	5	3.2	82.00

At the new level of output, the optimal combination of labor and capital is . The cost-minimizing ratio of labor to capital to produce 40 pizzas is the cost-minimizing ratio needed to produce 20 pizzas. This is always true of production functions that exhibit returns to scale.

On the following graph, use the blue line (circle symbol) to show the long-run total cost function by plotting the minimum total costs associated with producing 20 and 40 pizzas, based on your answers to the previous questions.