Q1. Consider a monopolist which produces two different products, each having the followingdemand functions:91 = 14 — —P1,92 ₂ = 24 - 2₂2₁where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p₂represent their prices.The monopolist's joint cost function is given asC (91, 92) = 9+59192 +92/2.(b)State the first-order conditions for profit maximization. Find the productionlevels, 9₁ and 92, and the monopoly prices, p₁ and p2, that satisfy the conditions.

Given Demand function: q1=14-14p1 ......(1)and q2=24-12p1 ...... (2) Monopolist cost function: Cq1,q2=q12+5q1q2+q22 ......(3) We have to find the profit maximization level of quantities and prices. Since the cost function is joint so we need a joint profit function of the monopolist and the monopolist profit function is equal to total revenue (revenue from quantity 1 and quantity 2) minus total cost. πq1,q2=Rq1+Rq2-Cq1,q2 FOC: ∂π∂q1=0∂π∂q2=0 The revenue function: q1=14-14p1⇒4q1=56-p1⇒p1=56-4q1 (1.1)Multiplying by q1⇒p1q1=56q1-4q12⇒R(q1)=56q1-4q12 .....(4) Similarly q2=24-12p2⇒2q2=48-p2⇒p2=48-2q2 ... (2.1)⇒p2q2=48q2-2q22⇒Rq2=48q2-2q22 .....(5)Now, the Profit function: πq1,q2=56q1-4q12+48q2-2q22-q12+5q1q2+q22πq1,q2=56q1-5q12+48q2-3q22-5q1q2 ......(6) For the first-order condition: take the partial derivative of the profit function with respect to quantity because quantity q is the decision variable. ∂π∂q1=56-10q1-5q2Put ∂π∂q1=056-10q1-5q2=0 .......(6) And ∂π∂q2=48-6q2-5q1Put ∂π∂q2=048-6q2-5q1=0⇒5q1=48-6q2⇒10q1=96-12q2 .......(7)Solving equation 6 and equation 7 Substitute value of 10q1 from equation 7 into equation 656-(96-12q2)-5q2=0⇒-40+12q2-5q2=0⇒7q2=40⇒q2=407⇒q2=5.71 Putting the value of q2 in equation 7 q1=96-12×40710⇒q1=2.74Profit maximizing value of q1 is 2.74 and q2 is 5.71 Putting the value of q1 in equation (1.1) p1=56-4×2.74p1=45.04 Similarly Putting the value of q2 in equation 2.1 p2=48-2×5.71p2=36.58 Profit maximizing level of price p1 is 45.04 and p2 is 36.58

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Consider a monopolist which produces two different products, each having the following demand functions: 91 = 14-7P1₁ 92 = 24- -P2, where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p represent their prices. The monopolist's joint cost function is given as C (91, 92) = 9+59192 +93². (b) State the first-order conditions for profit maximization. Find the production levels, 9₁ and 92, and the monopoly prices, pi and p2, that satisfy the conditions.

Consider a monopolist which produces two different products, each having the following demand functions: 91 = 14-7P1₁ 92 = 24- -P2, where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p represent their prices. The monopolist's joint cost function is given as C (91, 92) = 9+59192 +93². (b) State the first-order conditions for profit maximization. Find the production levels, 9₁ and 92, and the monopoly prices, pi and p2, that satisfy the conditions.

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Chapter1: Making Economics Decisions

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Question

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Q1. Consider a monopolist which produces two different products, each having the following
demand functions:
91 = 14 — —P1,
92 ₂ = 24 - 2₂2₁
where 9₁ and 92 represent the output levels of product 1 and product 2 and p₁ and p₂
represent their prices.
The monopolist's joint cost function is given as
C (91, 92) = 9+59192 +92/2.
(b)
State the first-order conditions for profit maximization. Find the production
levels, 9₁ and 92, and the monopoly prices, p₁ and p2, that satisfy the conditions.

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