Q*=100−2(24)=52cap Q raised to the * power equals 100 minus 2 open paren 24 close paren equals 52 The equilibrium price is and the equilibrium quantity is units . 2. Elasticity: Measuring Responsiveness
Maximize U(x,y) subject to PxX+PyY=BMaximize cap U open paren x comma y close paren subject to cap P sub x cap X plus cap P sub y cap Y equals cap B
Just as consumers maximize utility, firms seek to maximize economic profit ( ). Profit is the difference between Total Revenue ( TRcap T cap R ) and Total Cost ( TCcap T cap C Π=TR−TCcap pi equals cap T cap R minus cap T cap C The Production Function Firms combine inputs—typically Labor ( ) and Capital ( )—to produce an output quantity (
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(Unit Elastic): The percentage change in quantity matches the percentage change in price exactly. 3. Consumer Theory and Utility Maximization microeconomics with simple mathematics pdf
), known as the Law of Demand. A simple linear demand equation looks like this: Qd=a−bPcap Q sub d equals a minus b cap P
Where $MU$ is (the additional satisfaction from one more unit). Calculating MU is simple subtraction:
With just these tools, you can solve 80% of real-world microeconomic problems, from pricing strategies to tax incidence.
While complex models exist, simple mathematics —algebraic equations, linear graphs, and basic derivatives—is enough to understand most foundational microeconomic principles. Q*=100−2(24)=52cap Q raised to the * power equals
How do consumers maximize utility (satisfaction) with limited income? How do firms maximize profits? How do supply and demand determine market prices?
) , which measures how much quantity demanded changes when the price shifts. The Midpoint Formula
Once these topics feel comfortable, you are ready to unlock the most important analytical tools the field has to offer.
Applying simple math to microeconomics transforms abstract theories into . For example, by using basic algebra, a policy analyst can predict exactly how much a Profit is the difference between Total Revenue (
are the partial derivatives of the utility function (Marginal Utilities): The Budget Constraint Consumers are constrained by their income ( ). If the price of good PXcap P sub cap X and the price of good PYcap P sub cap Y , the budget equation is:
Firms face the engineering reality of production and the financial reality of costs. Their ultimate goal is profit maximization. The Profit Equation ) is calculated as Total Revenue ( TRcap T cap R ) minus Total Cost ( TCcap T cap C π=TR−TCpi equals cap T cap R minus cap T cap C : The total money a firm brings in from sales. TR=P×Qcap T cap R equals cap P cross cap Q Total Cost ( TCcap T cap C ) : The sum of Fixed Costs ( FCcap F cap C
Usually downward sloping. If a product’s price ( ) increases, the quantity demanded ( Qdcap Q sub d ) decreases. Equation Example: