Suppose that the government introduces a tax on interest earnings. that is, borrowers face a real interest rate of r before and after the tax is introduced, but lenders receive an interest rate of (1 − x)r on their savings, where x is the tax rate. we will analyze what happens when the tax rate x increases from zero to some value greater than zero, with r assumed to remain constant. [hint: when x = 0, you would have a normal straight budget constraint like we’ve seen in the lecture.]
1.) show the effects of the increase in the tax rate on a household’s lifetime budget constraint. [hint: draw what the lifetime budget constraint looks like when x = 0. then show how that changes when x > 0.]
2.) suppose the household was initially a borrower when x = 0. graphically show how the increase in the tax rate x affect the optimal choice of consumption (in the current and future periods) and saving for this household. specifically, show how the income and substitution effects matter for your answer.
3.) suppose the household was initially a lender when x = 0. graphically show how the increase in the tax rate x affect the optimal choice of consumption (in the current and future periods) and saving for this household. specifically, show how the income and substitution effects matter for your answer.

The monthly sales for yazici​ batteries, inc., were as​ follows: month jan feb mar apr may jun jul aug sept oct nov dec sales 19 20 17 12 11 18 16 17 19 22 21 24 this exercise contains only parts b and c. ​b) the forecast for the next month​ (jan) using the naive method​ = nothing sales ​(round your response to a whole​ number). the forecast for the next period​ (jan) using a​ 3-month moving average approach​ = nothing sales ​(round your response to two decimal​ places). the forecast for the next period​ (jan) using a​ 6-month weighted average with weights of 0.10​, 0.10​, 0.10​, 0.20​, 0.20​, and 0.30​, where the heaviest weights are applied to the most recent month​ = nothing sales ​(round your response to one decimal​ place). using exponential smoothing with alpha ​= 0.40 and a september forecast of 21.00​, the forecast for the next period​ (jan) = nothing sales ​(round your response to two decimal​ places). using a method of trend​ projection, the forecast for the next month​ (jan) = nothing sales ​(round your response to two decimal​ places). ​c) the method that can be used for making a forecast for the month of march is ▾ a 3-month moving average a 6-month weighted moving average exponential smoothing the naive method a trend projection .

Which statement best defines tuition? tuition is federal money awarded to a student. tuition is aid given to a student by an institution. tuition is money borrowed to pay for an education. tuition is the price of attending classes at a school.

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.