Given the profit function = -500 + 200Q - 4Q^2, where Q corresponds to output, do...
Given the profit function = -500 + 200Q - 4Q^2, where Q corresponds to output, do the following:
(a) Find that value of Q that maximizes profit.
(b) How do you know that your value of Q maximizes profit?
(c) What is the maximum value of profit?
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Given the profit function = -500 +
200Q - 4Q^2, where Q
corresponds to output, do...
A firm’s profit function is given by π(q) = TR(q)-C(q) where TR is Total Revenue and C...
A firm’s profit function is given by π(q) = TR(q)-C(q) where TR is Total Revenue and C is total cost. If the profit function is π(q)=200q - (120+25q+25q^2), what is the output q , that maximizes the firm’s profit? What is the firm’s revenue, variable cost, and profit? Should the firm operate or shut down in the short run? (Hint: What is the condition for profit maximization?)
Suppose a company's revenue function is given by R(q) = - q° + 200q and its...
Suppose a company's revenue function is given by R(q) = - q° + 200q and its cost function is given by C(q) = 160 + 11q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q) B) How many items (in hundreds) need to be sold to maximize profits?...
1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q +...
1. Suppose a perfectly competitive firm has a cost function described by TC = 200Q + Q 2 + 225 Each firm’s marginal revenue is $240. a. Find the profit maximizing level of output. b. Is this a short-run or long-run situation? How do you know? c. Assuming that this firm’s total cost curve is the same as all other producers, find the long-run price for this good.
Given a perfectly competitive firm in the output market where: P0= exogenous price, C(Q) = cost...
Given a perfectly competitive firm in the output market where: P0= exogenous price, C(Q) = cost function where: C’ > 0, C” > 0. a)State the firm’s profit function in terms of Q. b)Find the F.O.C. that maximizes profits at Q*. c)Interpret the F.O.C. d)Find the S.O.C. that maximizes profits at Q*. e)Interpret the S.O.C. f)Find dQ*/dP0using the implicit function rule on the F.O.C. g)Interpret the derivative in (f) economically.
Q5. Given the following short-run production function (x = variable input, Q = output):...
Q5. Given the following short-run production function (x = variable input, Q = output): Q = 3x2 - 0.1x3 (a) Determine the marginal product function (MPx) and the average product function (APx ). (b) Find the value of x that maximizes Q. (c) Find the value of x for which MPx is maximum. (d) Find the value of x for which APx is maximum. (e) Determine the boundaries of the three...
12. Given the demand function is Q 180 5P, find the following: a The revenue finction...
12. Given the demand function is Q 180 5P, find the following: a The revenue finction b. The revnue maximizing output and price c. The own-price elasticity of demand at P $80 d. The level ofe and P where the own-price elasticity of demand (ED) is equal to one, in absolute value. What is the nature of total revenue when lEDl 1? 13. Assume that the demand function is Q demand at each of the following prices a. b. $7...
Given a perfectly competitive firm in the input and output markets where: P0= exogenous price, Q...
Given a perfectly competitive firm in the input and output markets where: P0= exogenous price, Q = f(L, K0) where dQ/dL > 0 and d2Q/dL2< 0, the cost function where: C(L, K0) = r0K0+ w0L; r0= exogenous rental rate of capital, K0= exogenous capital stock, and w0= exogenous wage. a)State the firm’s profit function in terms of L. b)Find the F.O.C. that maximizes profit at L*. c)Interpret the F.O.C. d)Find the S.O.C. that maximizes profit at L*. e)Interpret the S.O.C....
Demand function: P=20-Q Total Cost function: C=Q22 +8Q+2 1. What output maximizes total profit? What are...
Demand function: P=20-Q Total Cost function: C=Q22 +8Q+2 1. What output maximizes total profit? What are the corresponding values of price, profit, and total revenue (sales)? 2. What output maximizes sales, and what are the corresponding values of price, profit, and total revenue?
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
Exercise 6. Consider a firm with monopoly power that faces the demand curve P= 100 – 3Q +4A 1/2 and has the total cost...
Exercise 6. Consider a firm with monopoly power that faces the demand curve P= 100 – 3Q +4A 1/2 and has the total cost function C = 4Q+ 10Q + A where A is the level of advertising expenditures, and P and Q are price and output a. Find the values of A, Q and P that maximizes the firm's profit. b. Find the maximum level of profit.
Suppose a company's revenue function is given by R(q) = - q° + 200q and its cost function is given by C(q) = 160 + 11q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) MP(q) B) How many items (in hundreds) need to be sold to maximize profits?...
12. Given the demand function is Q 180 5P, find the following: a The revenue finction b. The revnue maximizing output and price c. The own-price elasticity of demand at P $80 d. The level ofe and P where the own-price elasticity of demand (ED) is equal to one, in absolute value. What is the nature of total revenue when lEDl 1? 13. Assume that the demand function is Q demand at each of the following prices a. b. $7...
A firm's production function is given by Q=2L"2 +31/2 where Q, L and K denote the number of units of outputs, labor and capital. Labor cost is $2 per unit, capital cost is $1 per unit and output sells at $8 per unit. Show that the profit function is 1=16L"2 + 24K12 - 2L-K and hence find the maximum profit and the values of Land K at which it is achieved. HINT: do not forget to check the second sufficient...
Exercise 6. Consider a firm with monopoly power that faces the demand curve P= 100 – 3Q +4A 1/2 and has the total cost function C = 4Q+ 10Q + A where A is the level of advertising expenditures, and P and Q are price and output a. Find the values of A, Q and P that maximizes the firm's profit. b. Find the maximum level of profit.
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