You work for a drug manufacturing company and holds a patent on Hair Grow, the w
ID: 1202418 • Letter: Y
Question
You work for a drug manufacturing company and holds a patent on Hair Grow, the worlds most famous effective drug for restoring hair. Your job is to analyze the pricing and investment decisions facing the firm. Your marketing group estimates that Hair Grown has the following demand: P=101 - .00002Q. 1. your marginal cost for producing a Hair Grow pill is $1. what is the profit maximizing price and quantity? what is your profit? 2. Suppose the production facility can only produce 1,000,000 pills. What is the optimal price and quantity given the production constraint? What are your profits? 3. Suppose that you could increase the capacity of your plant 3,000,000 pills within a 2 year period for a cost of $30,000,000. Should you undertake the investment (for simplicity, assume you can borrow the funds for the expansion at a 0 percent interest rate)?
Explanation / Answer
1. Demand is as follows -
P = 101 - 0.00002Q
Total revenue (TR) = P*Q = (101 - 0.00002Q)*Q = 101Q - 0.00002Q2
Marginal Revenue = dTR/dQ = d(101Q - 0.00002Q2)/dQ = 101 - 0.00004Q
Marginal cost = $1
Profit-maximizing condition -
MR = MC
101 - 0.00004Q = 1
Q = 2,500,000
P = 101 - 0.00002Q = 101 - 0.00002*2,500,000 = 101 - 50 = 51
Thus,
The profit-maximizing price is $51 per pill and profit-maximizing quantity is 2,500,000 pills.
Total revenue = P * Q = $51 * 2,500,000 = $127,500,000
Total Cost = MC * Q = $1 * 2,500,000
Profit = TR - TC = $127,500,000 - 2,500,000 = $125,000,000
The Total profit is $125,000,000 or $125 million.
2. It has been provided that production facility cam produce only 1,000,000 pills.
Calculate price given the production constraint -
P = 101 - 0.00002Q = 101 - 0.00002* 1,000,000 = 101 - 20 = 81
Thus,
The optimal price given the production constraint is $81 per pill and optimal quantity is 1,000,000 pills.
Total revenue, TR = P * Q = $81 * 1,000,000 = $81,000,000
Total Cost, TC = MC * Q = $1 * 1,000,000 = $1,000,000
Profit = TR - TC = $81,000,000 - $1,000,000 = $80,000,000
The Total Profit is $80,000,000 or $80 million.
3. When production increases to 3,000,000 pills.
P = 101 - 0.00002Q = 101 - 0.00002*3,000,000 = 101 - 60 = $41
Total revenue, TR = P * Q = $41 * 3,000,000 = $123,000,000
Total Cost, TC = MC * Q = $1 * 3,000,000 = $3,000,000
Profit = TR - TC = $123,000,000 - $3,000,000 = $120,000,000
The Profit after capacity increase would be $120,000,000 or $120 million.
So, in two years company could earn profit of $240 million. Since, the cost of expanding capacity is $30 million. Company can earn a net profit of $210 million by expanding capacity.
If company do not expand capacity and keep it at 1,000,000 pills per year then in two years, it can earn a profit $160 million.
Since, expansion results in an increase of $50 million in profit in two years, the company should undertake the investment.
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