Marginal Products, Hiring Decisions and Cost Functions (25 points)

Breadsmith produces bread loaves according to the function

q(K,L)=10K^(1/2)*L^(1/3)

K is the number of oven hours per week, L is the number of labor hours hired per week, and Lis the number of loaves produced per week.

a)(5 points) At the moment, Breadsmith has 2 ovens and can run each for 50 hours per week.Each bread loaf sells for $3.50. At what amount of labor hours would Breadsmith's value of their marginal product of labor exceed a $10/labor hour wage? A $15.00/labor hour wage? Discuss.

b)(5 points) Derive Breadsmith's short-run cost function for the $10 and $15/hour labor wage if it owns the two ovens, and the cost of running each oven is $10/hour.

c)(10 points) Suppose it costs $10/hour to run the ovens and $15/hour to hire workers in the long-run.Derive Breadsmith's long-run cost function.

d)(5 points) Does Breadsmith have increase, decreasing, or constant returns to scale? Justify your answer.