ECON 301 FINALLL WAZZUP:
Utility/Profit Maximisation

* Consumers maximise utility by expanding their purchases until the utility received from the last unit equals the price to be paid for this unit.
Producers maximise profits by expanding output until the price received for the last unit produced equals the cost incurred by producing this unit.

* Fixed cost FC does not vary with output (horizontal line) (pretend its $50) * VC=0 when Q=0 * TC curve is determined by VERTICALLY adding the FC curve to the VC curve * so the distance between TC curve and VC curve is FC * afc falls continuously from $50, as output (Q) increases.. AFC=FC/Q * whenever MC lies below AC, the AC curve falls * whenever AC is at a MIN, MC=AC *
Average-Marginal Relationship * ATC curve shows the total cost of production * The vertical distance between the ATC and AVC curves decreases as Q increases * The AVC curve reaches MIN point at a lower out than the ATC curve * This is because MC=AVC at its min point and MC=ATC at its min point * * * * Mc eventually rises with the quantity of output * ATC curve is USHAPED * MC curve crossed the ATC curve at the MIN of ATC
The ISOCOST line * Shows all possible combos of labor and capital that can be purchased for a given TC * C=wL+rK * For ever different level of cost, this equation descrives a diff. isocost line * Rewritten: K=C/r-(w/r)L * Isocost line has a slope of dK/dL=-w/r * Marginal rate of technical substatution of LABOR for CAPITAL is the negative of the slpe of the isoquant and is eual to the ratio of the marginal products of labor and capital * MRTS= -dK/dL=MPofL/MPofK * This means that when a firm minimized the cost of producing a particular output, the following condition holds: * MPl/MPk=w/r * eg. Cost minimizationg * L at w=10/hr K at r=20/hr C=10L+20K *
Economies and Diseconmoies of scale * As a firms output increases, the cost of produsing that output is lilely to decline, at least to a point because: * If the firm operates on a larger scale, workers can specialize in the activities at which they are most productive * Scale can provide flexibility. By varying the combo of inputs utilized to produces the firms output, managers can organized the production process more effectively * economies of scale: situation in which output can doubled for less than a doubling cost * diseconomies of scale: situation in whicj a doubling of output requires more than doubling of cost * Ec=(dC/C)/(dq/q)

ATC=TC/Q MC=dTC/dQ (change in total cost/change in quantity of output)
AFC=FC/Q
AVC=VC/Q

1. Deriving Slope when Two Independent Variables are Functions of a Third Variable

If you have a function such as:

w = xy

where

x = f(z) y = g(z)

the slope of w with respect to z can be found using the following equation:

dw/dz = (dx/dz)y + x(dy/dz).

For example, if

w = xy

and

x = z4 y = z2

dw/dz = (4z3)z2 + z4(2z) = 4z5 + 2z5 = 6z5

This is the same result you would have obtained if you had multiplied x by y before calculating the slope. That is, as

w =