4Suppose that the monthly supply and demand for widgets could be approximated as follows:

Supply: Qs = 4128 + 144P

Demand: Qd= 15488- 176P

where P is the unit price in dollars, and Q is the quantity of widgets in thousands of units per month.

(a) Calculate the equilibrium price and quantity that will prevail under a free market, and the price elasticity of supply and demand at the market equilibrium. (4 marks)

(b) Suppose the government imposes a price floor of $45 per unit. Calculate the changes in consumer and producer surplus, and the deadweight loss as a result of this policy. (8 marks)

(c) Suppose the government guarantees to purchase any excess supply to keep the price at $45 per unit. Calculate the total cost to the government and the resulting deadweight loss? (4 marks)

(d) Illustrate the demand and supply curves and your answers to parts (a), (b) and (c) in the SAME diagram. Make sure all curves, points, intercepts, and areas are properly labeled, with numerical values where appropriate. (4 marks)