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
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
