Jennys company produces biscuits at a constant cost of 6 eac

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).

Solution

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 .