Derive a firm’s supply curve. Now assume there are 200 firms selling strawberries at the Davis Farmers Market.

    April 21, 2024

ECN 100B Problem set 1
Question 1
 
 Imagine many small farms selling strawberries at the Davis Farmers Market, in a setting of perfect competition. Each individual firm faces costs C(q) = 100q2.
A. Derive a firm’s supply curve. Now assume there are 200 firms selling strawberries at the Davis Farmers Market.
 
B. Derive the market supply curve. Suppose the market demand curve is QD(p) = 1000 − 8p.
 
C. What are equilibrium price and equilibrium quantity?
 
D. Graph the inverse demand and inverse supply curves for the market andindicate the equilibrium price and quantity.  
 
E. What are consumer and producer surplus?
 
 Question 2 Imagine a CEO retreat in the desert in which CEOs spend hours in a sauna each day and cannot leave the desert between sauna sessions. The folks running the retreat (our firm) sell lemonade after each sauna session. They are a monopoly in the market of refreshments for this CEO camp in the desert. Imagine CEOs at the retreat have the inverse demand function p(Q) = 3600 − 600Q for lemonade after using the sauna. Furthermore, the folks running the retreat have the costfunction C(Q) = 300Q2 800 for lemonade.
 
A. What are equilibrium price and equilibrium quantity?
 
B. What is the folks running the retreat’s profit at the equilibrium?
 
C. Prove that this profit level is a global maximum.  
 
D. Show the equilibrium price and equilibrium quantity graphically. Include theinverse demand curve, firm’s marginal revenue curve, and firm’s marginal cost curve.
 
E. What are consumer surplus, producer surplus, and deadweight loss at theequilibrium?
 
Question 3
 
Now imagine that the government (of Mexico in this case, as it turns out) decides to tax lemonade using a specific tax of 1800 per unit of lemonade produced and sold.
 
A. What are the new post-tax equilibrium price and equilibrium quantity?
 
B. What is the folks running the retreat’s new profit at the equilibrium?
 
C. Prove that this new profit level is a global maximum.  
 
D. Show the new equilibrium price and equilibrium quantity graphically. Includethe inverse demand curve, firm’s marginal revenue curve, and firm’s pre- and post-tax marginal cost curves.
 
E. What are consumer surplus, producer surplus, and deadweight loss at theequilibrium? How have these quantities changed from the no-tax case in Question 2?
 
Question 4
 
The government of Mexico has decided it would rather ensure that there is no deadweight loss in this market for after-sauna lemonade at the CEO retreat by removing the tax and instead setting a price cap.
 
A. At what price should the government cap lemonade sales?
 
B. What are the new post-price cap equilibrium price and equilibrium quantity? C. What is the folks running the retreat’s new profit at the equilibrium? D. Prove that this new profit level is a global maximum.
 
E. Show the new equilibrium price and equilibrium quantity graphically. Includethe original and regulated inverse demand curves, firm’s marginal revenue curve, and firm’s marginal cost curve.
 
F. What are consumer surplus, producer surplus, and deadweight loss at theequilibrium? How have these quantities changed from the no-tax case in Question 2?
 
Question 5
 
Now imagine that the CEO retreat is a monopsony employer for laborers (to make lemonade) in the geographic market surrounding the retreat. Suppose the firm faces an inverse supply curve of labor of w(L) = 4000 1000L.
 
A. What is the marginal expenditure curve for the CEO retreat? Now assume the monopsony has an inverse demand curve for labor of w(L) = 13000−1000L.
 
B. What are the equilibrium wage and labor quantity?
 
C. Show the equilibrium wage and equilibrium labor quantity graphically.
 
 In-clude the inverse demand curve and the firm’s supply and marginal expenditure curves.
D. What are consumer surplus, producer surplus, and deadweight loss at theequilibrium? 6

Trust your assignments to an essay writing service with the fastest delivery time and fully original content.

July
January
February
March
April
May
June
July
August
September
October
November
December
2025
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
SunMonTueWedThuFriSat
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
00:00
01:00
02:00
03:00
04:00
05:00
06:00
07:00
08:00
09:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
Verified