A natural experiment is a chance occurrence that mimics a randomized controlled trial. In order to analyze causal effects from natural experiments, economists make use of a statistical method known as instrumental variables, in which one variable from a natural experiment is used as an instrument for a particular independent variable of interest. Assume the independent variable of interest is x1 and the dependent variable in a regression is y. Which of the following represent necessary characteristics of a suitable instrument? a. The instrument has at least 200 observations
b. The instrument is correlated with
c. The instrument has a conditional mean of zero
d. The instrument does not directly influence y, except through

On april 1, the cash account balance was $46,220. during april, cash receipts totaled $248,600 and the april 30 balance was $56,770. determine the cash payments made during april.

Oz makes lion food out of giraffe and gazelle meat. giraffe meat has 18 grams of protein and 36 grams of fat per pound, while gazelle meat has 36 grams of protein and 18 grams of fat per pound. a batch of lion food must contain at least "46,800" grams of protein and 70,200 grams of fat. giraffe meat costs $1/pound and gazelle meat costs $2/pound. how many pounds of each should go into each batch of lion food in order to minimize costs? hint [see example 2.]

Haley photocopying purchases a paper from an out-of-state vendor. average weekly demand for paper is 150 cartons per week for which haley pays $15 per carton. in bound shipments from the vendor average 1000 cartoons with an average lead time of 3 weeks. haley operates 52 weeks per year; it carries a 4-week supply of inventory as safety stock and no anticipation inventory. the vendor has recently announced that they will be building a faculty near haley photocopying that will reduce lead time to one week. further, they will be able to reduce shipments to 200 cartons. haley believes that they will be able to reduce safety stock to a 1-week supply. what impact will these changes make to haley’s average inventory level and its average aggregated inventory value?