Question

7. Long-run cost Suppose Ernie is opening a new restaurant that will produce pizzas using a combination of workers (L) and ovens (K). Ernie knows from experience that the total number of pizzas he can produce in an hour is given by the function q= 10K0.5 0.5 . Ernie can rent ovens for an hourly cost of $10 and must pay his employees $10 per hour. ($10 + K) * ($10 + L) Therefore, his total hourly cost function is given by TC = ($10+ $10) x ( K L) $10K + $10L Complete the following table by calculating the total cost of producing 20 pizzas per hour using 2 and 4 workers. Total Cost (TC) (Dollars) Pizzas per Hour Workers Ovens (q) (L) (K) 2014 2 2 .00 3 1 .33 1.00 1 worker, 4 ovens 40.00 L 4 workers, 1.00 ovens 4 50.00 3 workers, 1.33 ovens The cost-minimizing bundle of labor and capital used to produce 20 pizzas is 2 workers, 2.00 ovens 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 sto 1.00 th Suppose Ernie wants to double the number of pizzas he makes in an hour. 4.00 0.44 0.25

please complete the graph also..thank you!

Answer 1

+ $10L TC = $ 10 k Pizza L K TC Textio XL 3 se yo 10x3 + 10x1.33 = 43.3 20 1.33 20 50 20 4 1 overs est minimizing bundle 2 workess, 2 2= loks 0.5 MP = da = 1060s) kos 2-0.5 2 L me=de = 10(0.5) ko. o. du O RTS = = 2 = 2 = 1 loro.s) k l Tolos) kasos Rate of technical substitution of labor for capital is Pizzas co L 2 K 8 5.33 4o TC 2016) +8/10) = 100 83.30 4610) +4610) = 80 82 40 yo s 3.2 wookex, Govens the same constant

Plot (20,40) 2 (40,80) wo 20