A consumer must spend all of her income on two goods (X and Y). In each of the following scenarios, indicate whether the equilibrium consumption of goods X and Y will increase or decrease. Assume good X is a normal good and good Y is an inferior good. a. Income doubles.
b. Income quadruples and all prices double.
c. Income and all prices quadruple.
d. Income is halved and all prices double.

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

Mikkelson corporation's stock had a required return of 12.50% last year, when the risk-free rate was 3% and the market risk premium was 4.75%. then an increase in investor risk aversion caused the market risk premium to rise by 2%. the risk-free rate and the firm's beta remain unchanged. what is the company's new required rate of return? (hint: first calculate the beta, then find the required return.) do not round your intermediate calculations.

Which of the following statements is (are) true? i. free entry to a perfectly competitive industry results in the industry's firms earning zero economic profit in the long run, except for the most efficient producers, who may earn economic rent. ii. in a perfectly competitive market, long-run equilibrium is characterized by lmc < p < latc. iii. if a competitive industry is in long-run equilibrium, a decrease in demand causes firms to earn negative profit because the market price will fall below average total cost.