2. Suppose breakfast cereal has just been invented and is sold only by o company
ID: 1131227 • Letter: 2
Question
2. Suppose breakfast cereal has just been invented and is sold only by o company, Toast. Suppose: Demand: P=$24 _ (1 /4)Q: Qd =96-4P Toast's total cost function: C-$72 + (1/4Q2. ne a.) Graph the market below. What price and quantity does Toast choose? What are consumer surplus and producer surplus? What is Toast's profit? b.) Now multiple competitors begin selling N different cereal brands and when they do, demand for any one brand (such as Toast brand) is given by: P-24/NN-(1/4)0 where Q is the quantity sold by that brand. Toast's total cost function is still given by C = $72+ (1/4)Q: No other company is allowed to make Toast brand, but competing brands do lower demand for Toast brand, because a larger N shifts down Toast's demand curve. What profit does Toast make, as a function of N? use space on next page too.Explanation / Answer
2 a)
We have only one firm in this market it is a Monopoly. To find profit maximizing price and quantity we have MR=MC
P*Q= 24Q-0.25Q^2 , MR = 24-0.5Q and C= 72+0.25Q^2 & MC = 0.5Q
MR=MC ; 24-0.5Q = 0.5Q ; Q =24 ; P = 18
Consumer Surplus will be CS= 6*24*0.5 = 144*0.5=72
Profit = TR-TC = 18*24 - (72+0.25*576) =432-216 =216
Answer for b)
As we hae presence of N competitors here Profit maximization condition would be P=MC (competetive enviornemnt)
P=24/N^(0.5)-0.25Q & MC =0.5Q
24/N^0.5 = 0.75 Q
24/0.75Q =N^0.5
32/Q =N^0.5
1024/N =Q^2 and Q =32/N^0.5
Profit = TR-TC =PQ - 72+0.25Q^2 = 24/N^(0.5)Q-0.25Q^2-72-0.25Q^2 =24/N^0.5Q-72-0.5Q^2=24/N^0.5*32/N^0.5-0.5(1024/N)-72=768/N-512/N-72=256/N-72
Answer for C) Hence Profit would be 0 when N=32/9 =3 approx.
Long Run Price P =24/3^0.5-0.25(32/3^0.5) =16/3^0.5
and Quantity is 8/3^0.5
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