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Exam (elaborations)

Foundations of Mathematical Economics By Michael Carter

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Foundations of Mathematical Economics By Michael Carter

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  • September 11, 2024
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Solutions Manual Foundations of Mathematical
Economics By Michael Carter


Cobb-Douglas function - ANSWER:Q=f(K,L), Quantity= a function of capital and labor

Profit function - ANSWER:Profit (K,L) = PQ - (rK+wL)

Level curves - ANSWER:A line joining points of equal elevation on a surface
Obtained by intersecting the graph of f with a horizontal plane z=c and then
projecting into the (x,y) plane

Production theory - ANSWER:The principles in which the business has to decide on
how much of each commodity to sell and how much K,L it uses
Q=KL

Consumer theory - ANSWER:How people decide to spend their money

Partial differentiation - ANSWER:Differentiating an equation with more than one
parameter by just one

Chain rule - ANSWER:dy/dx = dy/du x du/dx

Product rule - ANSWER:f'(x) = uv' + vu'

Quotient rule - ANSWER:f'(x) = (uv'-vu')/v²

Production function - ANSWER:The relationship between quantity of inputs used to
make a good and the quantity of output of that good
The partial derivatives dq/dk and dq/dl of a production function q=f(k,l) are called
the marginal products or labour and capital
they describe how much output increases by if k or l increase by a small amount

The marginal product - ANSWER:The slope of the function in the L or K direction
Use f''(x) if you want to know if MP is increasing

Diminishing productivity of labour - ANSWER:The more L used, the smaller the
increase in Q when 1 more unit is added

Direct second order derivatives - ANSWER:Differentiate twice with respects to the
same parameter

Cross second order partial derivatives - ANSWER:Differentiate first with respects to X
then Y

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