Consider the constant-elasticity demand function Q = p^−ε, where ε > 0. a. Solve for the...
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![=> MR = P [el] - PR & It is given anat a is constant and hence](http://img.homeworklib.com/questions/a6bdc630-71bc-11ea-b96f-3594bde3b543.png?x-oss-process=image/resize,w_560)
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Consider the constant-elasticity demand function Q = p^−ε,
where ε > 0.
a. Solve for the...
Show that the demand function, Q=aP^b , a. Is a constant elasticity demand curve. b. The...
Show that the demand function, Q=aP^b , a. Is a constant elasticity demand curve. b. The vertical distance between the (inverse) demand and marginal revenue curves is a constant ratio of the price level for each value of quantity
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)...
1) Given the following demand function Q=8.5-p+0.1y a) Derive a formular for the price elasticity of...
1) Given the following demand function Q=8.5-p+0.1y a) Derive a formular for the price elasticity of demand and income elasticity of demand. b) find the elasticity if p=6 and y=1000 c) what will happen to price elasticity of demand if income varies. d) what will happen to income elasticity of demand if income varies. e) derive the total revenue function. show that the relationship between price and revenue depends on elasticity (Assume y = 0).
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?
Inverse demand function is given as P=$100,000 - 52.5Qd, where Qd is the annual quantity demanded....
Inverse demand function is given as P=$100,000 - 52.5Qd, where Qd is the annual quantity demanded. development costs were substantial and marginal costs for a treatment are "just" $750 per treatment. a) if you set a single price to maximize profits, what quantity will you supply annually? (hint: the marginal revenue function has the same y-axis intercept as the inverse demand function, but twice the slope. set MR=MC and solve for Q) b) what is the price for treatment (hint:...
You are a monopolist in a market with an inverse demand curve of: P=10-Q. Your marginal...
You are a monopolist in a market with an inverse demand curve of: P=10-Q. Your marginal revenue is: MR(Q)=10-2Q. Your cost function is: C(Q)=2Q, and your marginal cost of production is: MC(Q)=2. a) Solve for your profit- maximizing level of output, Q*, and the market price, P*. b) How much profit do you earn?
Suppose a monopolist faces the constant price elasticity demand curve: p = Q? where ? <...
Suppose a monopolist faces the constant price elasticity demand curve: p = Q? where ? < 0. The monopolist has a constant marginal cost of c. a. If ? < -1, can you determine what price and quantity will the monopolist set? Explain. b. If 0>?>-1, what is the price and quantity the monopolist will set?
Consider the relationship between monopoly pricing and the price elasticity of demand. If demand is...
Consider the relationship between monopoly pricing and the price elasticity of demand.
If demand is inelastic, total revenue would increase when a monopolist result, total cost would quantity at which the demand curve is inelastic. its price. As a produce a . Therefore, a monopolist will produce a quantity at which the demand curve is inelastic.
Use the purple segment (diamond symbols) to indicate the portion of the demand curve that is inelastic. (Hint: The answer is related...
Show work please A monopolist's inverse demand function is P= 150 – 3Q. The company produces...
Show work please
A monopolist's inverse demand function is P= 150 – 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2: a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q1 + Q2 = Q.) MR(Q) = 150-C6 Q4-06 Q2 b. Determine the profit-maximizing level of output for each facility. Output for...
Exercise 7. Elasticity and Revenue (Constant Elasticity Demand) The market demand function is X(p) = 100/p2....
Exercise 7. Elasticity and Revenue (Constant Elasticity Demand) The market demand function is X(p) = 100/p2. What is the elasticity, ε(p)? If p=1, what is market demand, X? What is sales revenue R=p∙X? If price increases to p’=2, what is X’? What is R’? The natural logarithm of the market demand is ln(X) = ln(100) -2ln(p). Take the derivative of ln(X) with respect to ln(p). What is ∂ln(X)/∂ln(p)? How does it compare to the elasticity result you found in part...
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?
Consider the relationship between monopoly pricing and the price elasticity of demand.
If demand is inelastic, total revenue would increase when a monopolist result, total cost would quantity at which the demand curve is inelastic. its price. As a produce a . Therefore, a monopolist will produce a quantity at which the demand curve is inelastic.
Use the purple segment (diamond symbols) to indicate the portion of the demand curve that is inelastic. (Hint: The answer is related...
Show work please
A monopolist's inverse demand function is P= 150 – 3Q. The company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1) = 6Q1, and the marginal cost of producing at facility 2 is MC2(Q2) = 2Q2: a. Provide the equation for the monopolist's marginal revenue function. (Hint: Recall that Q1 + Q2 = Q.) MR(Q) = 150-C6 Q4-06 Q2 b. Determine the profit-maximizing level of output for each facility. Output for...
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