ECN100B Problem Set 1 - Imagine many small farms selling strawberries

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