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A firm determined that its total cost of production is TC = 200 + 20Q + 5Q2. The marginal cost to produce the 10th unit is?

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Related questions

The White Company is a member of the lamp industry, which is perfectly competitive. The price of a lamp is $50. The firm's total cost and marginal cost functions are:

TC = 1000 + 20Q + 5Q2

MC = 20 + 10Q

where TC is total cost and MC is marginal cost (in dollars) and Q is hourly output.

a. What output maximizes profit?

b. What is the rm's economic pro t at this output?

c. What is the firm's average cost at this output?

d. If other firms in the lamp industry have the same cost function as this firm, is the industry in equilibrium? Why or why not?

A firm's total cost function is given by the equation TC = 4000 + 5Q + 10Q2 and marginal cost is given by the equation MC=5+20Q.

(A) Write an expression for each of the following cost concepts:

a. Total Fixed Cost

b. Average Fixed Cost

c. Total Variable Cost

d. Average Variable Cost

e. Average Total Cost

(B) Calculate the values of marginal cost and the costs in (a)-(e) above for Q=0,1,2,3.

(C) Determine the quantity that minimizes the average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds.

A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)

The Chief Executive Officer will manage the firm, choosing output and price. Currently, the CEO is negotiating an incentive-based contract with the shareholders of the company.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)

Hint: since the plan creates incentives for the CEO to maximize revenue rather than profit, you should not set MR = MC at this point. BIG hint: revenue is maximized when selling an additional unit won't increase your revenue, or in math terms, when MR = 0.)

Owners' proposal: CEO keeps 10% of TR.

Firm price:

  

Firm output:

  

Total revenue:

  

Firm profit:

  

CEO compensation:

  

Remaining profit for owners:

  

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