What does correlation does not imply causation mean? Give an example of two real-life variables that are correlated but do not have a causal relationship. Also give an example of two variables that are correlated and that also have a causal relationship.
17. Suppose that limn70 An = L. a.) Prove that if an > 0 for all ne N, then L > 0. b.) Give an example to show that an > 0 for all n E N does not imply that L >0.
tarks) Does A - B = imply B - A = 0? If so, prove it. If not, give a counterexample.' A-B=0 means A=B
1. 2. Give a counter example to show that linear independence usually doesn’t imply orthogonality. In the space of F3X3 with F either R or C, is the subset of matrices with all entries in the last row equal to zero a subspace? Justify your answer.
Show that gcd(a, b) = 1 and gcd(a, c) = 1 imply that ged(a, bc) = 1.
What is the Coase Theorem? What does this imply about the necessity of government corrections to markets that suffer from an externality problem? When will the theorem fail?
2. (5 Points) Boundary conditions generally imply for all z and t. For this, assume that ki > 0 and 0 < < 2π. Create a series of mathematical arguments with valid justifications to show that ki = K2 13, δ1 =82=dg, and Al +Ag=Ag.
Correlation does not imply nts O O A. linearity O B. significance O c. causation O D. bias O
1- If a firm experiences diminishing marginal productivity, does this imply that they experience diseconomies of scale? Explain. 2- Allocative efficiency in perfectly competitive markets depends on the assumption that marginal cost to firms equals marginal cost to society. Using gasoline as an example, what might be some social costs that are not included in the marginal cost to the firm? Explain.
1- If a firm experiences diminishing marginal productivity, does this imply that they experience diseconomies of scale? Explain. 2- Allocative efficiency in perfectly competitive markets depends on the assumption that marginal cost to firms equals marginal cost to society. Using gasoline as an example, what might be some social costs that are not included in the marginal cost to the firm? Explain