Jenny\'s company produces biscuits at a constant cost of $6 each. The company ha
ID: 1258483 • Letter: J
Question
Jenny's company produces biscuits at a constant cost of $6 each. The company has 2 groups of buyers-rich with demand Qrich = 2000 - P, and poor with demand Qpoor=2000-2P. Calculate profit-maximizing price, quantity, and profits, assuming that it is illegal/impossible to segregate the two groups of buyers. Calculate profit-maximizing price, quantity, and profits, assuming that it is legal/possible to segregate the two groups of buyers. Consider a monopoly facing inverse demand function: p (y)= 16-y, and with total Cost TC = 4y. Find optimal level of production and price. Illustrate optimal choice in the depicting Consumer, Producer Surplus and DWL (Dead Weight Loss).Explanation / Answer
Solution :
17
a) The total demand for rich and poor = (2000 - P ) + ( 2000-2P)
Total demand = 4000 - 3P
Profit is maximized when marginal revenue = marginal cost
Revenue = price X quantity demanded
R = P(4000-3P)
R = 4000P - 3P2
Marginal revenue = 4000 - 6P
4000-6P = 6
P = 665.67
Qunaity demanded = 4000 - 3 X P
Quantity demanded = 2003 units
b) If it is possible to seperate the two groups of buyers
Q(rich) = 2000 - P
Revenue = 2000 P - P2
Marginal revenue = 2000 - 2P
2000 - 2P = 6
Price (rich) = $ 997
Quantity demanded of rich = 2000 - 997
Q(rich) = 1003 units
Quantity demanded of poor = 2000-2P
Revenue = 2000P - 2P2
Marginal revenue = 2000 - 4P
2000-4P = 6
Price (poor) = $ 498.50
Quantity demanded of poor =2000 - 2 X $ 498.50
Quantity demanded of poor = 1003 units .
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