Where $MU$ is (the additional satisfaction from one more unit). Calculating MU is simple subtraction:

100−2P=-20+3P100 minus 2 cap P equals negative 20 plus 3 cap P 120=5P120 equals 5 cap P P*=24cap P raised to the * power equals 24 Now, substitute back into either equation to find Q*cap Q raised to the * power

$$\pi = \textTotal Revenue - \textTotal Cost$$ $$\pi = (P \cdot Q) - TC$$

: A concise lecture-style PDF covering "Microeconomics 1 Mathematics," including monotonic functions, slopes as rates of change, and first-order conditions for optimization. Free Open-Source Textbooks Principles of Microeconomics (OpenStax)

Suppose a market has the following demand and supply functions: Qd=100−2Pcap Q sub d equals 100 minus 2 cap P Qs=10+4Pcap Q sub s equals 10 plus 4 cap P To find the equilibrium price, set Qdcap Q sub d Qscap Q sub s 100−2P=10+4P100 minus 2 cap P equals 10 plus 4 cap P Bring all terms with to one side and constants to the other: 90=6P90 equals 6 cap P P*=15cap P raised to the * power equals 15 Now, substitute back into either the demand or supply equation to find Q*cap Q raised to the * power

: The cost of producing one more unit, found by taking the first derivative of the Total Cost function:

MUxPx=MUyPythe fraction with numerator cap M cap U sub x and denominator cap P sub x end-fraction equals the fraction with numerator cap M cap U sub y and denominator cap P sub y end-fraction Or, rearranged to show the optimization condition:

: Evaluating the "additional" cost or benefit of one more unit, often simplified as the slope of a line. NEW- Micro Unit 1 Summary- Basic Economic Concepts

A will provide tables of numbers, asking you to find the utility-maximizing combination given a budget. This is purely arithmetic.

) : Consumers are relatively insensitive to price changes. Essential goods like medicine often fall into this category. Unit Elastic (

Free PDF available, which provides a balance of conceptual understanding and straightforward mathematical application.

At its heart, microeconomics describes how markets reach equilibrium. We represent these using linear equations. : Typically expressed as is the quantity demanded, is the price, and represents the sensitivity of consumers to price changes. Supply Equation : Typically expressed as is the quantity supplied. Market Equilibrium : This occurs where Example Calculation :If Set them equal: back in to find 2. Consumer Theory and Utility Maximization

: A single seller controls the market face down an inverse demand curve where price depends on quantity ( ). Because selling more requires lowering the price, MRcap M cap R drops faster than price ( ). The firm still solves

ΔQΔPthe fraction with numerator cap delta cap Q and denominator cap delta cap P end-fraction

Consumers aim to maximize utility (satisfaction) given a limited budget. Simple math helps us map out their constraints and choices. The Budget Line