# Since the proof of the method is identical in both

• Notes
• 6

This preview shows pages 2–5. Sign up to view the full content.

. Since the proof of the method is identical in both cases, we shall not repeat it here, but simply refer you to the text. In Figure M.6-1, we have used the same labelling system as in Figure A.4-2 (page 597 of the text), with the horizontal intercept of the tangent to the supply curve at C labelled E and the vertical intercept labelled A . Just as with the price elasticity of demand, the price elasticity of supply s = EC/AC = OF/AF = EG/OG. (M.6.3) M6-2 MATH MODULE 6: ELASTICITIES P P P F F F S S S C C C S' S' S' O O O = A = E A A E E G G G Q Q Q (a) Inelastic supply (b) Elastic supply (c) Unitary elasticity of supply FIGURE M.6-1

This preview has intentionally blurred sections. Sign up to view the full version.

Notice, however, that here the directed line segments all go in the same direction, so that (as we would expect) s is positive. In Figure M.6-1 (a), notice that all three ratios are < 1: supply is inelastic. In Figure M.6-1 (b), all three ratios are > 1: supply is price-elastic. And in (c), both A and E coin- cide with the origin: all of the ratios are equal to 1, and the supply curve has unitary price elasticity at C . Application 2: Supply Elasticity: The “Eyeballing” Method If an exact numerical value for price elasticity of supply is not required, then Figure M.6- 2 provides a simple method for gauging whether supply is elastic, inelastic, or of uni- tary elasticity. If the tangent to the supply curve at a point C intersects the vertical axis in the positive quadrant, then supply is elastic at C. If it intersects the horizontal axis in the positive quadrant, then supply is inelastic at C. And if the tangent at C passes through the origin , then ( regardless of its slope ) the supply curve at C has unitary price elasticity. Application 3: Price, Elasticity, and Marginal Revenue In the text (p. 363), we derive the following relation between price ( P ), price-elasticity ( ) and marginal revenue (MR): MR = P (1 + 1/ ), or equivalently, P = MR [ /( + 1)]. (M.6.4) We can use Figure M.6-3 to illustrate one implication of Equation M.6.4. With one exception, if we know any two of the 4 variables P , MR, and the vertical intercept A , we can calculate the other two. To see why, note that = OF/AF and P = OF , so that MR = OF (1 + AF/OF ) = OF + AF = OF – FA. What this says is that A P = P – MR, or MR = 2 P – A , or P = ( A + MR)/2, or (in other words) that P is midway between MR and the MATH MODULE 6: ELASTICITIES M6-3 P O Q C 3 C 2 C 1 ε S > 1 ε S = 1 ε S < 1 FIGURE M.6-2
vertical intercept ( A ). For example, if the vertical intercept of the tangent to the demand curve is at \$24/kg when P = \$16/kg, then = OF/AF = 16/(16–24) = –2, and MR = 2 P – A = 2(16) – 24 = \$8/kg. The one exception occurs if we are given that MR = 0 and = –1, since these 2 val- ues of these variables are consistent with an infinite number of combinations of P and A : all we know is that A = 2 P.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern