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Microeconomics: Pricing and output decisions in Short run

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1. If a representative firm with total cost given by TC = 20 + 20q + 5q2 operates in a competitive industry where the short-run market demand and supply curves are given by QD = 1,400 - 40P and QS = -400 + 20P, the number of firms operating in the short run will be:

2. If the profit-maximizing markup price is marginal cost times 2, the elasticity of demand must be:

3. A representative firm with short-run total cost given by TC = 50 + 2q + 2q2 operates in a competitive industry where the short-run market demand and supply curves are given by QD = 1,690 - 40P and QS = -390 + 20P. Its short-run profit-maximizing level of output is:

4. The XYZ Steel Company produces its own coal for use in its production facility. The demand for steel is given by Ps = 500 - 2Qs and the total cost of producing steel is given by TCs = 100Qs, where Qs is tons of steel per week. The price of coal in a perfectly competitive market outside the firm is $250 per ton, and the total cost of producing coal is given by TCc = 40 + 5Qc2, where Qc is tons of coal per week. How much steel should the XYZ Company produce?

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See the attached file. Thanks!

Intra-firm pricing
1. If a representative firm with total cost given by TC = 20 + 20q + 5q2 operate in a competitive industry where the short-run market demand and supply curves are given by QD = 1,400 - 40P and QS = -400 + 20P, the number of firms operating in the short run will be:

A representative firm is a competitive firm will be a price taker firm. First, calculate the equilibrium price in the market by equating the demand and supply
QD=QS
1400-40P=-400+20P
60P=1800
P=30
Q=1400-40*30=200
For profit maximization: MC=MR=P
MC=dTC/dq = 20+5*2q=20+10q
Equating MC=MR, we get
20+10q=30
10q=10
q=1
Number of firms operating in the industry = Q/q = ...

Solution Summary

This post solves four different microeconomics problems related to market structure and pricing. First, problem shows how to calculate the number of firms operating in an industry in short run, second problem is about profit maximizing mark up pricing, third one is on short run profit maximizing output in a competitive market and the last one is about profit maximizing output.

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Long Run costs and Output Decisions

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

1. The following problem traces the relationship between firm decisions, market supply, and market equilibrium in a perfectly competitive market.

a. Complete the following table for a single firm in the short run:

Output TFC TVC TC AVC ATC MC
0 $300 0
1 100
2 150
3 210
4 290
5 400
6 540
7 720
8 950
9 1240
10 1600

b. Using the information in the table, fill in the following supply schedule for this individual firm under perfect competition, and indicate profit (positive or negative) at each output level. Hint: at each hypothetical price, what is the MR of producing one more unit of output? Combine this with the MC of another unit to figure out the quantity supplied.

Price Quantity Supplied Profit
$50
70
100
130
170
220
280
350

c. Now suppose there are 100 firms in this industry, all with identical cost schedules. Fill in the market quantity supplied at each in this market:

Price Market Quantity Supplied Market Quantity Demanded
$50 1,000
70 900
100 800
130 700
170 600
220 500
280 400
350 300
d. Fill in the blanks: From the market supply and demand schedules in c., the equilibrium market price for this good is _____ and the equilibrium market quantity is ____. Each firm will produce a quantity of ___and earn a ___(profit/loss) equal to ____.

e. In d., your answers characterize the short run equilibrium in this market. Do they characterize the long-run equilibrium as well? If yes, explain why. If no, explain why not (that is, what would happen in the long run to change the equilibrium and why?)

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