Suppose that we have a standard classical production function F(K, L) that exhibits constant returns to scale. Define output per worker as the ratio between output and labor: (F(K, L))/L. Prove (using the Euler equation) that, ceteris paribus, higher population causes average labor productivity to fall, i. e. show that ((∂) (F (K, L))/L)/∂L < 0.

Euler equation: F(K, L) = (MPK x K) + (MPL x L)

Who is not spending wisely? erika goes shopping and saves her receipts. she totals how much she spent and writes it down. mia needs to buy a new pair of shoes because she joined the soccer team. she looks at newspaper ads to find the best price. lauren has been thinking about getting a puppy for a long time. she walks by the pet store at the mall and decides to get a puppy. erin makes a purchase online using a credit card. she knows that she can pay the entire bill when it arrives.

Reliability and validity reliability and validity are two important considerations that must be made with any type of data collection. reliability refers to the ability to consistently produce a given result. in the context of psychological research, this would mean that any instruments or tools used to collect data do so in consistent, reproducible ways. unfortunately, being consistent in measurement does not necessarily mean that you have measured something correctly. to illustrate this concept, consider a kitchen scale that would be used to measure the weight of cereal that you eat in the morning. if the scale is not properly calibrated, it may consistently under- or overestimate the amount of cereal that’s being measured. while the scale is highly reliable in producing consistent results (e. g., the same amount of cereal poured onto the scale produces the same reading each time), those results are incorrect. this is where validity comes into play. validity refers to the extent to which a given instrument or tool accurately measures what it’s supposed to measure. while any valid measure is by necessity reliable, the reverse is not necessarily true. researchers strive to use instruments that are both highly reliable and valid.

Bandar industries berhad of malaysia manufactures sporting equipment. one of the company’s products, a football helmet for the north american market, requires a special plastic. during the quarter ending june 30, the company manufactured 35,000 helmets, using 22,500 kilograms of plastic. the plastic cost the company $171,000. according to the standard cost card, each helmet should require 0.6 kilograms of plastic, at a cost of $8 per kilogram. 1. what is the standard quantity of kilograms of plastic (sq) that is allowed to make 35,000 helmets? 2. what is the standard materials cost allowed (sq x sp) to make 35,000 helmets? 3. what is the materials spending variance? 4. what is the materials price variance and the materials quantity variance?