Refer to Scenario 15.5. Suppose there are 100 firms each with a short run total cost of TC = q2 + q + 4, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 − 50P, how much will be produced in the market ( Call this Q)? and what profit will each firm make?Group of answer choicesQ=300, Profit = $25Q=400, Profit = $15Q=500, Profit = $21Q=600, Profit = $50
Question
Refer to Scenario 15.5. Suppose there are 100 firms each with a short run total cost of TC = q2 + q + 4, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 − 50P, how much will be produced in the market ( Call this Q)? and what profit will each firm make?Group of answer choicesQ=300, Profit = 15Q=500, Profit = 50
Solution
To solve this problem, we first need to find the equilibrium price and quantity in the market.
- Find the market supply curve:
Since the marginal cost (MC) is equal to the firm's supply, we have MC = 2q + 1. Solving for q gives us q = (MC - 1)/2.
Since there are 100 identical firms in the market, the market supply Qs is 100q. Substituting q into this gives us Qs = 100(MC - 1)/2 = 50MC - 50.
- Set market supply equal to market demand to find the equilibrium price:
We have QD = 1050 - 50P and Qs = 50MC - 50. Setting these equal to each other gives us 1050 - 50P = 50MC - 50.
Substituting MC = 2q + 1 into this gives us 1050 - 50P = 50(2q + 1) - 50. Simplifying this gives us 1050 - 50P = 100q.
Solving for P gives us P = 21 - 2q.
- Substitute P into the demand equation to find the equilibrium quantity:
Substituting P = 21 - 2q into QD = 1050 - 50P gives us Q = 1050 - 50(21 - 2q). Simplifying this gives us Q = 50q.
- Find the profit for each firm:
Profit = Total Revenue - Total Cost.
Total Revenue = P*q = (21 - 2q)*q = 21q - 2q^2.
Total Cost = q^2 + q + 4.
So, Profit = 21q - 2q^2 - (q^2 + q + 4) = 20q - q^2 - 4.
From the options given, none of them match the calculations. There might be a mistake in the problem or the answer choices.
Similar Questions
Suppose there are 100 firms each with a short run total cost of STC = q2 + q + 10, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 - 50P, profit to the firm will beQuestion 3Select one:a.9.b.15.c.5.d.6.
Suppose there are 100 firms each with a short run total cost of STC = q2 + q + 10, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 - 50P, what is the equilibrium price?Question 5Select one:a.50.b.10.c.5.d.11.
Suppose a chemical company is in a perfectly competitive industry and has a short run total cost curve of TC = 1/3q3 + 5q2 + 10q + 10 and a short run marginal cost of SMC = q2 + 10q + 10. At the price of 49, how many will be produced?Question 4Select one:a.3.b.15.c.0.d.5.
Suppose there are 100 firms each with a short run total cost of STC = q2 + q + 10, so that marginal cost is MC = 2q +1. The market supply curve isQuestion 2Select one:a.QS = -100 + 100Pb.QS = -0.5 + 0.5Pc.QS = -50 + 50P2d.QS = -50 + 50P
Refer to Scenario 15.1. A monopolist has total cost TC = Q2 + 10Q + 100 and marginal cost MC = 2Q + 10. It faces demand Q = 130- P (so its marginal revenue is MR = 130 - 2Q). Its profit-maximizing output and profit are respectivelyGroup of answer choicesQ=30 and $1,700Q=25 and $ 2,500Q=20 and $450Q=10 and $1,300
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.