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# most cost-efficient way

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1.BJORN SELLS TENNIS LESSONS TO 2 DISTINCT GROUPS OF CUSTOMERS: "ADULTS" AND "YOUTHS". HE CAN EASILY DISTINGUISH BETWEEN THE 2, AND THE LESSONS ARE CERTAINLY NON-TRANSFERABLE. HIS TOTAL COST FUNCTION IS TC = 100 + 8Q,
WHERE TC IS MEASURED IN DOLLARS PER DAY AND Q IS THE TOTAL NUMBER OF STUDENTS "SERVED" THAT DAY(COST IS SAME TO BJORN WHETHER YOUTH OR ADULT). THE DEMAND FUNCITON FOR ADULT CUSTOMERS IS Qa = 25 - 0.25Pa (Pa = 100 - 4Qa) AND THE DEMAND FUNCTION FOR YOUTH IS Qy = 60 - Py(Py = 60 - Qy) WHERE Qa AND qY ARE, RESPECTIVELY, THE NUMBERS OF LESSONS FOR ADULTS AND YOUTHS DAILY, AND Pa ADN Py ARE THE PRICES CHARGED TO EACH GROUP FOR LESSONS. HINT: Q=Qa + Qy
A. WHAT IS THE MARGINAL COST TO BJORN OF PROVIDING THESE LESSONS/
MC = \$________PER LESSON B. IF BJORN WISHES TO MAXIMIZE HIS TOTAL PROFITS, WHAT PRICE SHOULD HE CHARGE EACH CLASSOF CUSTOMER, AND HOW MANY CUSTOMERS OF EACH GROUP CAN HE EXPECT TO SERVE DAILY? Pa = \$__________ Py = \$ _________ Qa = _______LESSONS PER DAY Qy = ________LESSONS PER DAY C. CALCULATE THE PRICE ELASTICITY OF DEMAND FOR EACH GROUP OF CUSTOMERS AT TEH PROFIT MAXIMUM VALUES OF PRICES AND QUANTITIES. FOR "ADULTS"_________ FOR "YOUTHS"_______________ IN GENERAL, ONE SHOULD EXPECT A PROFIT MAXIMIZING FIRM IN THIS SITUATION TO CHARGETHE HIGHEST PRICE T THE GROUP WHOSE DEMAND IS THE ______________(MOST/ORLEAST) ELASTIC WITH RESPECT TO PRICE. D. CALCULATE THE TOTAL DAILY PROFITS AT THE MAXIMUM.PROFITS = \$____PER DAY. E. CALCULATE THE CONSUMERS SURPLUS FOR EACH GROUP; ADULTS =_____ YOUTHS =___________TOTAL =________

2.NOW SUPPOSE, ACCORDING TO A NEW LAW THAT BJORN IS NOT PERMITTED TO PRICE DISCRIMINATE BETWEEN THESE TWO GROUP. IN EFFECT THEN HE FACES A SINGLE MARKET IN WHICH HE WILL CHARGE A SINGLE PRICE. FIND THE PROFIT-MAXIMIZING PRICE AND QUANTITY. HINT(S) 1. IF YOU'VE WORKED THIS AS AN ECONOMIC PROBLEM, THE NEW (TOTAL) DEMAND FUNCTION IS Q=85 - 1.25P, SO THEINVERSE DEMAND FUNCTION IS P=68 - 0.8Q.IF YOU WORKED THIS WITH EXCEL SOLVER, SIMPLY ADD THE CONSTRAINT THAT THE TWO PRICES MUST BE EQUAL. PRICE = \$_______PER UNIT, Q = _________LESSONS PER DAY PROFITS = \$_______PER DAY, A. RECALCULATE TEH CONSUMERSSURPLUS FOR EACH GROUP SEPARATELY(USING THE SAME DEMAND CURVES AS BEFORE) AND TOTAL THE RESULTS. ADULTS = \$___________ YOUTHS = \$___________
TOTAL = \$__________ B. WHO'S BEEN HELPED AND WHO'S BEEN HURT BY THIS NEW LAW? BY HOW MUCH? C.DO YOU THINK IT WAS GOOD FOR "SOCIETY AS A WHOLE" TO FOR BID BJORN FROM PRICE DISCRIMINATING BETWEEN ADULTS AND YOUTHS?(THIS ISREALLY A MATTER OF OPINION;BUT I MUST HAVE A REASONALE, COHERENT ANSWER)

3. INDIA, INC.SELLS ITS PRODUCT IN A MARKET WHERE THE DEMAND IS GIVEN BY THE FOLLOWING: LN(Q)=22.1 -3.0*LN(P). (WHERE LN(Q) =THE NATURAL LOGARITHM OF Q A. WHAT IS THE OWN PRICE ELASTICITY OF DEMAND?_____ B. THE FIRMS MARGINAL COST IS \$120 PER UNIT, WHAT PRICE SHOULD INDIA CHARGE FOR ITS PRODUCT IF IT WISHES TO MAXIMIZE ITS PROFITS?___ WHAT "MARKUP" OVER MARGINAL COST DOES THIS REPRESENT? P = \$ ________PER UNIT MARKUP = ______%

4. AN EXCLUSIVE TENNIS CLUB CURRENTLYCHARGES ITS MEMBERS A \$200 MONTHLY MEMBERSHIP FEE.IN ADDITION, MEMBERS PAY A \$12 COURT FEEEVERY TIME THEY PLAY TENNIS. THE TYPICAL MEMBER, OR PROSPECTIVE MEMBER, HAS THE FOLLOWING DEMAND FUCTION FOR VISITS TO THE CLUB: Qi = 12 - 0.5P OR(P = 24 -2Qi) WHERE P IS THE COURT FEE AND Qi IS THE NUMBER OF TIMES MEMBER"i" VISITS TEH CLUB PER MONTH. THE MARGINAL COST TO THE LCUB O FPROVIDING SERVICES TO THIS CUSTOMER IS \$6 PER VISIT. AS THE CLUB'S NEW MANAGER,WHAT CHANGES WOULD YOU RECOMMEND IN THEMONTHLY MEMBERSHIP FEE AND THE COURT FEE, IF THE CLUB WISHES TO MAXIMIZE PROFITS?? RECOMMENDED MEMBERSHIP FEE = \$______________PER MONTH RECOMMENDED COURT FEE = \$_____VISIT

5. CANDI KEYNES RUNS A SPECILA PHONE SERVICE FOR PEOPLE WHO LIKE TO CALL AND TALK ABOUT ECONOMICS. SUPPOSE HER TYPICAL CUSTOMER HAS THE FOLLOWING WEEKLY DEMAND FUNCTION: Qi = 100 -20P (P= 5 -0.05Qi) WHERE P IS THE PRICE PER MINUTE AND Qi IS AMOUNT OF TIME, IN MINUTES , THE CUSTOMER WOUDL WISH TO PURCHASE PER WEEK AT THIS PRICE. HER COST FUNCTION IS TC = 2000 + 2*Q WHERE TC IS THE COST OF OPERATIONS, IN DOLLARS PER WEEK , AND Q IS THE TOTAL NUMBER OF MINUTES OF SERVICE PROVIDED PER WEEK(I,E., SUMMED UP OVER HER 100 CUSTOMERS). CURRENTLY , SHE CHARGES \$3.50 PER MINUTE. ASSUME MS. KEYNES HAS 100 CUSTOMERS(ALL WITH THE SAME DEMAND FUNCTION AS ABOVE), AND CALCULATE HER CURRENT WEEKLY PROFIT. \$________PER WEEK
SHE IS CONSIDERING ABANDONING HER PRICING SCHEME INFAVOR OF A NEW ONE IN WHICH SHE SELLS HER CUSTOMERS LARGE BLOCKS OF TIME FOR SOME AMOUNT IN ADVANCE(SAY, 30 MINUTES FOR \$100), GIVEN THE TYPICAL CUSTOMER ABOVE, WHAT WOULD BE THE MOST PROFITABLE BLOCK OF TIME TO SELL , AND WHAT WOULD BE THE MAXIMUM PRICE SHE WOULD BE ABLE TO CHARGE FOR THAT AMOUNT OF TIME? ______________ MINUTES FOR \$___________. UNDER THIS NEW PRICING SCHEME FOR MS. KEYNES, CALCULATE HER WEEKLY PROFITS \$____________PER WEEK.

6. FO RTHE FOLLOWING SIMULTANEOUS-MOVE GAME,
A. CIRCLE ANY PAIR OF STRATEGIES THAT CORRESPONDS TO A NASH EQUILIBRIUM:
UP-LEFT..... UP-RIGHT
DOWN-LEFT DOWN-RIGHT
FIRM#2
LEFT RIGHT
FIRM
#1 UP 100,70 0,0

DOWN 130,30 50,100

B. DOES EITHER FIRM POSSESS A DOMINANT STRATEGY?(CIRCLE ONE)
I.YES, ONLY FIRM #1
IIYES, ONLY FIRM #2 DOES
III YES, THEY BOTH DO
IV. NO, NEITHERFIRM HAS A DOMINANT MOVE STRATEGY.

C. IF FIRM #1 WERE ALLOWED TO MAKE THE FIRST MOVE, SO THAT THIS JUST BECAME A SEQUENTIAL-MOVE GAME, WHAT WOULD BE THE SUB-GAME PER FECT(ROLLBACK) EQUILIBRIUM? (CIRCLE ONE) UP-LEFT, UP-RIGHT, DOWN-LEFT, DOWN-RIGHT. D. SKETCH THE DECISION TREE IN THE SPACE BELOW(ASSUMING FIRM #1GETS TO MAKE THE FIRST MOVE.

7.SUPPOSE A FIRMS PRODUCTION FUNCTION IS Q= K(1/3)L(2/3), AND SUPPOSE THAT THE COST OF CAPITAL IS Pk = \$10/UNIT WHILE THE COST OF LABOR(THE WAGE)IS \$20/LABOR-HOUR. THE PRODUCT IS SOLD ON A COMPETITIVE MARKET FOR Pq = \$50 PER UNIT A. IN THE SHORT RUN, SUPPOSE CAPITAL IS FIXED AT K = 27,000 UNITS/MONTH. IF L = 8,000 LABOR-HOURS/MONTH, WHAT IS THE MONTHLY RATE OF OUTPUT? PROFITS??
Q = _________UNITS PER MONTH
PROFITS = \$__________PER MONTH
B. ASSUMING STILL THAT K IS FIXED AT 27,000 UNITS/MONTH, WHAT LEVEL OF L WOULD MAXIMIZE PROFITS IN THE SHORT RUN? wHAT WOUDL BE THE RATE OF OUTPUT?? PROFITS??
L = _______LABOR-HOURS PER MONTH
Q = ________UNITS PER MONTH
PROFITS = \$ ___________PER MONTH
C. SUPPOSE TAHT, IN THE LONG RUN, THE FIRM MAINTAINS THE OUTPUT RATE AT Q = 50,000 UNITS PER MONTH. aSSUMING THE COSTS OF CAPITAL AND LABOR DO NOT CHANGE, WHAT WOULD BE THE MOST COST-EFFICIENT WAY IN THE LONG-RUN TO PRODUCE 50,000 UNITS PER MONTH??
K = __________UNITS PER MONTH
L = __________LABOR HOURS PER MONTH
PROFITS = \$__________PER MONTH

https://brainmass.com/economics/keynes/most-cost-efficient-way-153188

#### Solution Summary

The most cost-efficient way is determined in the cases.

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