Suppose the production function for high-quality Brandy is given by: q=K^1/2L^1/2, where q is the output of brandy per week and L is labor hours per week. In the short run, K is fixed at 100, so the short run production function is: q=10L^1/2.
a) If capital rents for $10 each and wages are $5 per hour, show that the short run total costs are: STC=1000 + .05q^2
b) how much will the firm produce at a price of $20 per bottle of brandy? How many labor hours will be hired per week? What profit will the firm make? Explain