Question

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2. (30 points) Jerry is a self-employed message therapist working from home. All of his costs are fixed, which means that to maximize his profit, all he needs to do is maximize revenue. Suppose that Jerry faces the following yearly demand function for an hour session: Q = 2,500 – 10P. a. Graph Jerry's demand function b. What is the profit-maximizing price Jerry should charge for his services? How many sessions will he do at this price? Show this point on the graph and shade the region that corresponds to Jerry's revenue. c. What is the elasticity of demand at Jerry's optimal price and quantity? d. For a generic revenue function, R(Q) = P(Q)*Q, the first derivative with respect to quantity (aka marginal revenue) is: MR= dR dP de = do* Q + P Using this fact, demonstrate whether the fact you found for part c holds true for revenue maximization in general (Hint 1: Remember how to maximize revenue).

Answer 1

Part (e.) let's Total look into Revenue price is aty curve demand curve e th Elastic demand se unit elastic y Inelastic B graph -4 hwerwe pont A : Maximum total Revenue DE aty demand graph 2 from our question: means we are at graph 2, So if the will FALL We has a unit elasticity that point Q in graph I and en point A on prices were to increase the Tolne Revenu Now if the demand was inelastic that means we are at are At in graph 2 then the increase in prices I will lead to a fall in Total Revenue and similarity for the cluste region increase in price will increase TR.

Partlf) MC= $20 fer session 25 ITR = P Q = f( 2500 - 10P) - = 25001 - 1012 Q = 2500-10P lop = 2500-Q. P = 2500 - 10 TR = (2500 -alo = 2500 - IMR = 250 - 2 = 250-G казать - то H = 250 Q- Q? max profit an o - 10 02 20 250 - 20 10 - 20 Q = 0 = 0 2.50 - Q- 20 5 1250 - Q-100Q 12.50 101 o 2-3 unity

- 2500- 12-3 P = 248.77 (g.) MR - ap & Qtp - P (dx 8 & 10 al do do Xal 6 e - for Put equation into MR = P (1-1) profits to be maximum MR=MC 1 (1 - 1) = me Ple-1) - MC P = ( e me MR = MC D (kopit maximisation, For e> be elasticity 1 ELASTIC DEMAND