Derive the Marginal Rate of Substitution between Consumption and Leisure for the following utility functions. a. K(CL) = 50 × C × L ( 2 points)
b. H(C, L) = 100 × C 2 × L 3 ( 2 points)
c. J(C, L) = 250 × ln(CL) (2 points) (d) U(C, L) = 120 × (ln(C 2 ) + ln(L))
d. There are 52 weeks in a year. Assume that the price of consumption is equal to 1 dollar per unit of consumption and that the wage is 1000 dollars per week. Assume that the individual receives 4000 dollars in non-labor income.

Required:
Determine which of the above utility functions represent the same set of preferences, and for those utility functions that represent the same set of preferences, determine the optimal bundle of consumption and leisure as well as the number of weeks worked.

On january 1, 2017, fisher corporation purchased 40 percent (90,000 shares) of the common stock of bowden, inc. for $980,000 in cash and began to use the equity method for the investment. the price paid represented a $48,000 payment in excess of the book value of fisher's share of bowden's underlying net assets. fisher was willing to make this extra payment because of a recently developed patent held by bowden with a 15-year remaining life. all other assets were considered appropriately valued on bowden's books. bowden declares and pays a $90,000 cash dividend to its stockholders each year on september 15. bowden reported net income of $400,000 in 2017 and $348,000 in 2018. each income figure was earned evenly throughout its respective year. on july 1, 2018, fisher sold 10 percent (22,500 shares) of bowden's outstanding shares for $338,000 in cash. although it sold this interest, fisher maintained the ability to significantly influence bowden's decision-making process. prepare the journal entries for fisher for the years of 2017 and 2018. (if no entry is required for a transaction/event, select "no journal entry required" in the first account field. do not round intermediate calculations. round your final answers to the nearest whole dollar.)

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 .

Suppose that real interest rates increase across europe. this development will u.s. net capital outflow at all u.s. real interest rates. this causes the loanable funds to because net capital outflow is a component of that curve.