# Week 3 Assignment

By vixendkb
Apr 27, 2015
497 Words

BUS640: Managerial Economics

Professor John Sellers

Problem 1:

a Which inputs are fixed and which are variable in the production function of William’s pizza shop? Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed? Fixed: Oven costs; building costs; normal utility costs.

Variable: # of workers; raw material costs; electricity costs; per unit costs. b What number of workers appears to be most efficient in terms of pizza product per worker? Six workers produce an average of 190 pizzas.

c What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week? Again, six workers. The rate for each is the same, so minimal cost per pizza is the same as production per worker. d Why would marginal productivity decline when you hire more workers in the short run after a certain level? Training time needed to bring workers to efficient status, along with their experience. Salary costs are up front and prior to full efficiency point. e How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer. As far as number of workers, the range between 2-5 workers provides fairly consistent production numbers, and you can reasonably assume that profit per pizza is equal or more up to the level of five workers. Problem 2

a Describe and derive an expression for the marginal cost (MC) curve. Slope of the TVC which is positive and roughly 20. The actual derivative formula for MC=20+.016Q b Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes). The incremental cost can be determined by plugging in the incremental number of pairs being 200, so you get MC=20+.016 x 200=23.2. Add in the 2000 per week, and the total cost is 2023.2 c What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output. We already know that MC=20+.016Q

P=(4100-Q)/25

TR= Q x (4100-2Q)/25

MR= (4100-2Q)/25 = 820-.08Q

20+.016Q = 820 - .08Q

800 = .096Q

Q = 800/.096 = 8333.33

d) Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation. By distinguishing between short and long run, the short run profits are maximized at Q = 8333.33, any expansion would not maximize profits. The firm thinks that the long run is likely to go up, then it could consider an expansion and a new lease would be required. The cost of a new lease is 2000 justified only when demand might rise.

References

Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint Education. This text is a Constellation™ course digital materials (CDM) title.

BUS640: Managerial Economics

Professor John Sellers

Problem 1:

a Which inputs are fixed and which are variable in the production function of William’s pizza shop? Over what ranges do there appear to be increasing, constant, and/or diminishing returns to the number of workers employed? Fixed: Oven costs; building costs; normal utility costs.

Variable: # of workers; raw material costs; electricity costs; per unit costs. b What number of workers appears to be most efficient in terms of pizza product per worker? Six workers produce an average of 190 pizzas.

c What number of workers appears to minimize the marginal cost of pizza production assuming that each pizza worker is paid $500 per week? Again, six workers. The rate for each is the same, so minimal cost per pizza is the same as production per worker. d Why would marginal productivity decline when you hire more workers in the short run after a certain level? Training time needed to bring workers to efficient status, along with their experience. Salary costs are up front and prior to full efficiency point. e How would expanding the business affect the economies of scale? When would you have constant returns to scale or diseconomies of scale? Describe your answer. As far as number of workers, the range between 2-5 workers provides fairly consistent production numbers, and you can reasonably assume that profit per pizza is equal or more up to the level of five workers. Problem 2

a Describe and derive an expression for the marginal cost (MC) curve. Slope of the TVC which is positive and roughly 20. The actual derivative formula for MC=20+.016Q b Describe and estimate the incremental costs of the extra 200 pairs per week (from 1,000 pairs to 1,200 pairs of shoes). The incremental cost can be determined by plugging in the incremental number of pairs being 200, so you get MC=20+.016 x 200=23.2. Add in the 2000 per week, and the total cost is 2023.2 c What are the profit-maximizing price and output levels for Paradise Shoes? Describe and calculate the profit-maximizing price and output. We already know that MC=20+.016Q

P=(4100-Q)/25

TR= Q x (4100-2Q)/25

MR= (4100-2Q)/25 = 820-.08Q

20+.016Q = 820 - .08Q

800 = .096Q

Q = 800/.096 = 8333.33

d) Discuss whether or not Paradise Shoes should expand its output further beyond 1,200 pairs per week. State all assumptions and qualifications that underlie your recommendation. By distinguishing between short and long run, the short run profits are maximized at Q = 8333.33, any expansion would not maximize profits. The firm thinks that the long run is likely to go up, then it could consider an expansion and a new lease would be required. The cost of a new lease is 2000 justified only when demand might rise.

References

Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint Education. This text is a Constellation™ course digital materials (CDM) title.