Question

QUESTION 1 James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = (1 + Q2 where Q1 and Q2 denote the quantities of rolls and pies respectfully. If P1 and P, denote the corresponding prices, then the inverse demand equations are: Q1 = 70 – P1 and 0.5Q2 = 100 – P2

REQUIRED:

a) If James decides to charge the same price for rolls and pies per day (that is, P1 = P2), how many of rolls and pies in total should he make in order to maximize the profit of a particular day?

b) If James decides to charge different prices as above for rolls and pies per day (that is, P1 # P2), how many of rolls and pies should he make in order to maximize the profit of a particular day?

c) Which of the above options (a) or (b) is more profitable? Provide the rationale for your answer.

Answer 1

Given : TC = 900+50Q

Then, MC = dTC/dQ = 50

Now, Q1 = 70-P1 or, P1 = 70-Q1

Then, MR1 = 70-2Q1

Again, 0.5Q2 = 100-P2 or, P2 = 100-0.5Q2

Then, MR2 = 100-Q2

a) If P1=P2

Total demand Q = Q1+Q2

or, Q = 70-P+200-2P (where P=P1=P2)

or, Q = 270-3P

or, P = 90-(Q/3)

Then, MR = 90-(2Q/3)

Now, for profit maximization,

MR=MC

or, 90-(2Q/3)=50

or, 2Q/3 = 40

or, Q = 60 units

and P = 90-(Q/3) = 90-(60/3) = $70

Here, profit = total revenue - total cost

or, profit = (P*Q)-(MC*Q) (neglecting total fixed cost)

or, profit = ($70*60)-($50*60)

or, profit = $1,200

b) If P1P2,

then, for profit maximization, MR1=MR2=MC

Now, MR1=MC

or, 70-2Q1=50

or, Q1=10 units

and P1=70-Q1=70-10 = $60

Again, MR2=MC

or, 100-Q2=50

or, Q2=50 units

and P2=100-(0.5Q1)=100-(0.5*50) = $75

Then, profit = total revenue - total cost (neglecting total fixed cost)

or, profit = (P1*Q1)+(P2*Q2)- (MC*Q) (where Q=Q1+Q2)

or, profit = ($60*10)+($75*50)-($50*60)

or, profit = $1,350

c) From a and b, we can see, price discrimination is more profitable (case b). This is because the firm can charge higher price in a low elastic sub-market and lower price in a high elastic sub-market thereby, increasing its revenue (and profit) .