6. (14 points total) One of the businesses in Smalltown, IN is Debbie’s Greenhou

Question

6. (14 points total) One of the businesses in Smalltown, IN is Debbie’s Greenhouse specializing in growing irises and tulips. Debbie sells them to flower shops all across Indiana. The cost of raising each flower is 20 cents, plus Debbie has to pay $3000 annually to cover the cost of the capital equipment she uses and the energy costs. Usually, the annual demand for her flowers is given by      QD = 100,000 – 100,000 P, which can also be rewritten as an inverse demand relationship, 000100, 1 QP = . a. (10 pts) Currently, Debbie produces 50,000 flowers a year. What price should she charge to ensure she sells them all?      

(10 pts) What is her current profit?

(12 pts) Does she maximize her profit? Explain how you arrived at the answer.

d. (12 pts) Debbie could sell her business for $20,000, invest that money at 5% APY, and take a parttime $15,000/yr barista job at her friend’s coffee shop. She would end up working the same number of hours she is currently working. Given the availability of this opportunity, what is her economic profit from her flower business?            

Explanation / Answer

(a)

QD = 100,000 – 100,000 P

QS = Number of flowers supplied = 50,000

Equilibrium is when QD = QS

100,000 – 100,000 P = 50,000

P = (100,000 - 50,000) / 100,000 = 0.50

(b)

Current profit = Revenue - Costs

=(50,000 x $0.5) - ($3000 + $0.20 x 50,000)

= $25,000 - $13,000

= $12,000

(c) The profit-maimizing price & output is found by equating MR with MC.

P = (100,000 - Q) / 100,000

Revenue, TR = P x Q = (100,000Q - Q2) / 100,000

Marginal revenue, MR = dTR / dQ = (100,000 - 2Q) / 100,000

Marginal Cost = Cost of raising each flower = 0.20

Equating MR with MC:

(100,000 - 2Q) / 100,000 = 0.20

100,000 - 2Q = 20,000

2Q = 80,000

Q = 40,000

P = (100,000 - Q) / 100,000 = (100,000 - 40,000) / 100,000

= 0.60

So, Profit when Q = 40,000 & P = 0.60

= (40,000 x $0.60) - ($3,000 + $0.20 x 40,000)

= $24,000 - $11,000

= $13,000

So, currently Debbie is not maximizing profit.

(d)

Interest Debbie can earn by selling the flower business = $20,000 x 5% = $1,000 per year

So, Economic profit from flower business = Current profit - implicit costs

= $12,000 - $1,000 - $15,000

= - $4,000 (Economic Loss)

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