A monopolist produces its good according to the cost function C(q) = cq, where q is...
A monopolist produces its good according to the cost function C(q) = cq, where q is the quantity it produces. the price it receives for the good, p, is given by the inverse demand function
p(q) = a-bq. the monopolist also pay a per-unit tax of t on each unit of the sold, Assume a, b, c, and t are positive constants and a > c+t.
question:
(a) Find the monopolist's optimal choice of q and the associated values of p and profits(as functions of a,b,c and t)
(b) Find dp/dt. what portion of the tax is passed on to consumers? ( hint: good interpretation of dp/dt gives you the answer)
Homework Answers
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A monopolist produces its good according to the cost function
C(q) = cq, where q is...
A monopolist faces inverse demand P = on TC(Q) = cQ. (a) Find the optimal price,...
A monopolist faces inverse demand P = on TC(Q) = cQ. (a) Find the optimal price, P, and quantity, QM (b) Solve for the monopolist's optimal profits, TM (c) Graph the equilibrium and show consumer surplus, producer surplus and deadweight loss. Be 150 -3Q and total cost functi careful with the marginal cost curve. (d) Compute CS and PS. These will be functions of the cost parameter c. (e) Compute DWL. Similarly, it will be functions of the cost parameter...
3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand...
3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand is given by PD (q) = 10 – 2q. There are no other pre-existing distortions in the market. (a) What is the privately optimal quantity and price chosen by the monopolist? For parts (b) and (c), assume that a tax of $t is imposed on every unit of output produced by the monopolist. (b) Derive the optimal quantity and price chosen by the monopolist...
3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand...
3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand is given by pºq) = 10 - 2q. There are no other pre-existing distortions in the market. (a) What is the privately optimal quantity and price chosen by the monopolist? For parts (b) and (c), assume that a tax of $t is imposed on every unit of output produced by the monopolist. (b) Derive the optimal quantity and price chosen by the monopolist as...
A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a)...
A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a) Show that the demand elasticity is -e (b) Find the firm's optimal price as a function of c and ε. (c) What happens to price as є ічі.e. є approaches 1 from the right side of the number line)? (d) What is the monopoly's profit-maximizing output?
The inverse demand function for good X supplied by a monopolist is given by the formulaP(Q)...
The inverse demand function for good X supplied by a monopolist is given by the formulaP(Q) = a – bQ (usual notation). The marginal production cost of the monopolist is constant and equal to c (a > c). Find by how much will the monopolist’s output change in the equilibrium in two cases: (i) when the government introduces a quantity tax t, (ii) when the government supports the monopolist with a quantity subsidy s. a) Upon the tax the output...
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of...
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of unit electricity is denoted by pe. Suppose that the market demand is given by q 1. Write down the monopolist's profit maximization problem. 2. Draw MC(), MR(a), 3. Determine the optimal levels of production gMand pricePe 4.lustrate that the monopolist price is higher than the competitive equilibrium price and pelin a same figure. PC pe
1. The inverse demand function for a good takes the constant elasticity form p(Q) = Qβ...
1. The inverse demand function for a good takes the constant elasticity form p(Q) = Qβ , −1 < β < 0, which is a commonly used simple functional form. The good is produced by n identical firms with a cost function c(qi) = cqi . Note that c 0 (qi) = c and c 00(qi) = 0; i.e., there are constant marginal costs. A specific tax of t per unit is imposed on the production of the good. (a)...
Microeconomics [20] A monopolist with cost function c(Q) demand functions are given by. faces a consumer...
Microeconomics
[20] A monopolist with cost function c(Q) demand functions are given by. faces a consumer whose Q1=20-P and Q2-40-2P. (a) [5] Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. come) associated with this pricing strategy, if any? optimal third-degree price-discrimination strategy. Which consumer is (b) [5] What is the deadweight loss (relative to the competitive market out- (c) [5] Now, suppose price discrimination is possible. Find the...
1. [20] A monopolist with cost function c(Q) = 2 faces a consumer whose demand functions...
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have, it's That's really all I have, in fact, I've figured out the questions A,B,C, but...
have, it's That's really all I
have, in fact, I've figured out the questions A,B,C, but I don't
know how to approach the rest of the question.
Practice Problem 2: Crash Course in Optimization: Part II 1. Consider a monopolist who pays an output tax $t for each unit of output produced. Thus, total tax payments are simply tQ, where is the quantity produced. Suppose the government is considering increasing the tax. Some people have argued that, because the firm...
A monopolist faces inverse demand P = on TC(Q) = cQ. (a) Find the optimal price, P, and quantity, QM (b) Solve for the monopolist's optimal profits, TM (c) Graph the equilibrium and show consumer surplus, producer surplus and deadweight loss. Be 150 -3Q and total cost functi careful with the marginal cost curve. (d) Compute CS and PS. These will be functions of the cost parameter c. (e) Compute DWL. Similarly, it will be functions of the cost parameter...
3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand is given by PD (q) = 10 – 2q. There are no other pre-existing distortions in the market. (a) What is the privately optimal quantity and price chosen by the monopolist? For parts (b) and (c), assume that a tax of $t is imposed on every unit of output produced by the monopolist. (b) Derive the optimal quantity and price chosen by the monopolist...
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A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a) Show that the demand elasticity is -e (b) Find the firm's optimal price as a function of c and ε. (c) What happens to price as є ічі.e. є approaches 1 from the right side of the number line)? (d) What is the monopoly's profit-maximizing output?
, A profit-maximizing monopolist produces electricity. Its cost function is given by C(a)-6q The price of unit electricity is denoted by pe. Suppose that the market demand is given by q 1. Write down the monopolist's profit maximization problem. 2. Draw MC(), MR(a), 3. Determine the optimal levels of production gMand pricePe 4.lustrate that the monopolist price is higher than the competitive equilibrium price and pelin a same figure. PC pe
Microeconomics
[20] A monopolist with cost function c(Q) demand functions are given by. faces a consumer whose Q1=20-P and Q2-40-2P. (a) [5] Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. come) associated with this pricing strategy, if any? optimal third-degree price-discrimination strategy. Which consumer is (b) [5] What is the deadweight loss (relative to the competitive market out- (c) [5] Now, suppose price discrimination is possible. Find the...
1. [20] A monopolist with cost function c(Q) = 2 faces a consumer whose demand functions are given by. 01 20 P and Q2 40 2P. (a) 5] Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. (b) 15) What is the deadweight loss (relative to the competitive market out- come) associated with this pricing strategy, if any? (c) 15) Now, suppose price discrimination is possible. Find the monopolist's...
have, it's That's really all I
have, in fact, I've figured out the questions A,B,C, but I don't
know how to approach the rest of the question.
Practice Problem 2: Crash Course in Optimization: Part II 1. Consider a monopolist who pays an output tax $t for each unit of output produced. Thus, total tax payments are simply tQ, where is the quantity produced. Suppose the government is considering increasing the tax. Some people have argued that, because the firm...
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