SMALL INCREMENTS FORMULA + IMPLICIT DIFFERENTIATION+ TUTORIAL 3- UTILITY FUNCTIONS
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1
A curve has the equation y=2x^3 +3x^2 -12x. Use small increments formula to estimate changes in Y when X changes from i) 2 to 1.99 ii) 2 to 2.01. show working
check notes, answers should be -0.24 and 0.24. firstly differentiate, then put y= 2 into eq. then times by 0.01 to find difference (0.24)
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2
use answer from a) to estimate the value of y when x = 1.99 and 2.01
check notes for method, answer is 3.76 and 4.24
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3
IMPLICIT DIFF: find dy/dx if 8y^3 + 2x^2y - x = 60
check notes: -4xy-1/ 24y^2 + 2x^2
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4
Whats the equation for marginal rate of substitution?
\- MUx/ MUy or -MU1/MU2
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5
When we divide powers this is the same as…
minusing powers, e.g. x^8/x^5= x^3
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6
How do we check the law of diminishing utility
we differentiate twice, if the answer is less than zero then law of diminishing marginal utility holds. if it is above 0 then law of diminishing marginal utility doesn’t hold
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7
calculate the marginal utility from this utility function: u(x,y) = x^2/3y^4/5. then find law of diminishing returns for MUx and MUy. then calculate MRS
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