Managerial Economics & Business Strategy Chapter 1 The Fundamentals of Managerial Economics

Let’s try some homework (number 3) Suppose that the total benefit and total cost from an activity are, respectively, given by the following equations: B(Q) = Q-5Q 2 and C(Q) = 100+8Q n Write out the equation for net benefits n What are the net benefits when Q=1? Q=5? n Write out the equation for marginal net benefits n What are the marginal net benefits when Q=1? Q=5? n What level of Q maximizes net benefits? n At the value of Q that maximizes net benefits, what is the value of marginal net benefits?

Conclusion Make sure you include all costs and benefits when making decisions (opportunity cost). When decisions span time, make sure you are comparing apples to apples (PV analysis). Optimal economic decisions are made at the margin (marginal analysis).

Appendix A Calculus of Maximizing Net Benefits …And other useful Math stuff

Variables and Functions Variable n “Something” that can assume different values n Can be measured What does optimal mean?? n Best outcome possible given circumstances Doesn’t have to be the BIGGEST –Maximum profits but Minimum Cost Function n Mathematical depiction of the key components of a variable n TR = f(Q) Which is the independent variable? –Q–Q Which is the dependent variable? –TR

What are the pieces? Dependent Variable nYnY Independent Variable nXnX Y-intercept nana Slope nbnb What is slope???

Marginal Analysis Looks at the change in the dependent variable that results from a unit change in the independent variable PriceProfit  P  Q  Revenue  Cost  Profit

Why use Calculus?? Looks at rates of change in a continuous function n Assume economic variables are related to each other in a continuous fashion but are valid only at stated discrete intervals Calculus, first of all, is wrongly named. It should never have been given that name. A far truer and more meaningful name is “SLOPE-FINDING”. – Eli Pine’s How to enjoy Calculus Slope of a linear function n Constant n Y = mX + b Nice but…our functions are typically continuous

Derivatives The derivative of Y with respect to X n Slope of the tangent line to the point in question on the curve n d is used to mean changes in Y relative to very SMALL changes in X  is used to look at changes BETWEEN two points

Derivative RULES Constants n ALWAYS ZERO!!! What is the derivative of 10? –Zero Power Functions

More Rules Sums and Differences n The derivative of the sum (difference) is equal to the sum (difference) of the derivatives of the individual terms n If U=g(x) and V=h(x) then…

And more… Products n The derivative of the product of two expressions is equal to the first term multiplied by the derivative of the second, PLUS the second term times the derivative of the first

And more… Quotient n Denominator MULTIPLIED by derivative of the numerator MINUS numerator MULTIPLIED by the derivative of the denominator ALL DIVIVED BY the denominator squared

Divide by 10X

Total Revenue TR = 7Q – 0.01Q 2 What is the Marginal Revenue function? n MR = Q TC = 100 – 8Q + 10Q 2 What is the Marginal Cost function? n MC = Q