Suppose that each 0.1 percentage point decrease in the equilibrium interest rate induces a $10 billion increase in real planned investment spending by businesses. in addition, the autonomous spending multiplier is 2 2 and the money multiplier is equal to 3 3. furthermore, every $20 billion increase in the money supply brings about a 0.1 percentage point reduction in the equilibrium interest rate. how much must real planned investment increase if the fed desires to bring about a $ 200 billion increase in real gdp? $   (round your answer to a whole number.)what dollar amount of open market operations must the fed undertake to bring about the money supply change necessary to bring about a $ 200 200 billion increase in real   (round your answer to a whole number.)

David consumes two things: gasoline (g) and bread (b). david's utility function is u(g, b) = 10g^0.25 b^0.75. use the lagrange technique to solve for david's optimal choices of gasoline and bread as a function of the price of gasoline, p_g, the price of bread, p_b, and his income m. with recent decrease in the price of gasoline (maybe due to external shock such as shale gas production) does david increase his consumption of gasoline? for david, how does partial differential g/partial differential p_g depend on his income m? that is, how does david's change in gasoline consumption due to an increase in the price of gasoline depend on his income level? to answer these questions, find the cross-partial derivative, |partial differential^2 g/partial differential m partial differential p_g.