Imagine a town where there are only two cheese producers that supply all of the town's cheese. The first, MaPas Cheese, has its own cows but uses any cows milk to make their cheese. The second, Mystery Cheeses, uses a blend of 50% their own milk and 50% milk imported from other ranches; their cheese is a proprietary blend that they are famous for, and it is the only cheese that they make. There is also a third company in town, Milk Importers United, that can supply equivalent-quality milk after a 2 weeks notice. Explain in simple terms the effect on the demand and supply of the dairy economy of this small town when 25% of local cows die unexpectedly. New cows take a month to source.
If 25% of cows die in this town, it will have the following effect on all of the firms listed above: 1. Mystery Cheeses will experience a 25% decline in supply because of their proprietary blend. If they were simply creating cheese with any milk and not their own, then this hindrance would only cause them to lose 12.5% or less of their supply, but their recipe is dependent on their local population of cows. This supply decrease will be persistent until they can get new cows as there is no replacement for their on-site milk. 2. MaPa's Cheeses will have a 25% supply decline for 2 weeks until Milk Importers can begin supplying them until they get new cows. In addition to returning to normal supply levels, they will likely experience an increase in demand as locals buy more of their cheese in lieu of the 25% decline in Mystery Cheese supply. 3. Milk Importers United would experience an increase in demand as they try to fill the shortages of MaPa's Cheeses. This would be a relatively short lived demand shock though as the cheese produces would be able to acquire new cows within a months time, eliminating the need of imported milk.
What problems do Heteroscidasticity and Autocorrelation pose for Ordinary Least Squares analysis of a dataset?
Both Heteroscidasticity and Autocorrelation violate assumptions of the classical linear regression model that the Guass-Markov theorem requires to be true if Ordinary Least Squares will be the best unbiased and efficient linear estimator. Specifically, in order to use OLS on a dataset and have it be efficient and unbiased, it must meet some conditions: the sum of estimated values of x = true x, there is no covariance between residuals temporally, the variance of the dataset is constant, and there is no covariance between any of the explanatory variables and the residuals of the model. Heteroscidasticity is created when the variance is not constant, which violates the CLRM and makes estimates inefficient. This problem is caused primarily by miscalculation by statistical software and will lead to misestimated standard errors if not corrected for. Autocorrelation on the hand is caused by improper functional specifications that do not account for some temporally varying factor; this is a violation of intertemporal covariance of the residuals and also causes the estimates to be inefficient. Note that although both estimates would now be inefficient, they are still UNbiased in that neither causes a violation of the first and fourth rules listed above for the Gauss-Markov theorem. Based on these results, you could use the unbiased estimates, but constructing a proper confidence interval or any use of the standard errors would require transforming the model or the standard errors to precipitate usable answers.
Given a consumption budget constraint and an indifference curve between two goods for an individual, what does the tangent point of these curves represent?
Let's begin by breaking down our curves so that we can understand the functional relationships between the goods and between the curves for the consumer. The budget constraint is often represented as a negative linear relationship between the acquisition of two goods. In other words, given a set amount of money, all points on a consumer's budget constraint represent the different possible allocations of the consumer's money between the two goods. In Economics they refer to the slope of this curve as the Marginal Rate of Substitution between two goods and it represents the consumer's possibilities strictly in terms of budget. The indifference curve represents different allocations between two goods that will yield the same utility. The curve is convex to the origin, demonstrating marginal diminishing utility with respect to consuming all of either of the goods. All points on this curve represent the consumer's relative utility tradeoff between the two goods, with each point on a single curve denoting the same cardinal utility. The slope at each point gives the Marginal Rate of Transformation, which represents the utility relationship between the two goods as one consumes more or less of one of the goods. Because of the shape of the indifference curve, a consumer's utility will always be maximized per dollar by finding the specific level of indifference curve that will be tangent to the budget constraint. When a tangency is found, their slopes will be equal and the marginal rate of substitution will equal the marginal rate of transformation. An optimal consumption bundle will be achieved wherein the consumer is maximizing their utility between two goods given a set budget constraint.