A bakery store employs workers (W) and cake machines (M) to produce cake according to following...

 

Transcribed Image Text:

A bakery store employs workers (W) and cake machines (M) to produce cake according to following production 1 2 function: Q(M,W)=M³W³. The hourly cost of machines is $40 and the hourly cost of workers is $10. a) Set up the Lagrangian function for the cost-minimization of the store for a given production level Q*. Determine the optimal capital to labor ratio. Describe the long-run output expansion path. b) Suppose the manager wishes to produce 100 units of cake. How much labor and capital should s/he employ? How much will it cost to produce? c) Suppose that a new order arrives and the amount of pasta the manager needs to produce is now 225. Assuming s/he is unable to purchase more capital, how much will it cost to meet the new production level? d) In the long-run, the manager will be able to employ more capital as well as labor. If the manager continues to produce 225 units of output, how much will it cost in the long run? A bakery store employs workers (W) and cake machines (M) to produce cake according to following production 1 2 function: Q(M,W)=M³W³. The hourly cost of machines is $40 and the hourly cost of workers is $10. a) Set up the Lagrangian function for the cost-minimization of the store for a given production level Q*. Determine the optimal capital to labor ratio. Describe the long-run output expansion path. b) Suppose the manager wishes to produce 100 units of cake. How much labor and capital should s/he employ? How much will it cost to produce? c) Suppose that a new order arrives and the amount of pasta the manager needs to produce is now 225. Assuming s/he is unable to purchase more capital, how much will it cost to meet the new production level? d) In the long-run, the manager will be able to employ more capital as well as labor. If the manager continues to produce 225 units of output, how much will it cost in the long run?