Economists in the ministry of agriculture in kwale county have estimated the following market model for fertilizer based on annual time series data on price and quantity in thousands. The government intends to reduce the market price by 20% per bag as requested by farmers. Consequently, it will buy the excess output if any at the market equilibrium price. Alternatively, a new plant costing 20 million with a life time of 5 years, producing 5 million worth of fertilizer annually can be constructed. Assuming a 10% market rate of return, what should the county government do? Qd=36-1/3p. Qs= -

Question

Economists in the ministry of agriculture in kwale county have estimated the following market model for fertilizer based on annual time series data on price and quantity in thousands. The government intends to reduce the market price by 20% per bag as requested by farmers. Consequently, it will buy the excess output if any at the market equilibrium price. Alternatively, a new plant costing 20 million with a life time of 5 years, producing 5 million worth of fertilizer annually can be constructed.  Assuming a 10% market rate of return, what should the county government do?   Qd=36-1/3p.   Qs= -

anonymous · Answer

My attempt:
At equilibrium, Quantity supplied (Qs) = Quantity Demanded (Qd)
Therefore Qs= -9+1/2p = Qd=36-1/3p
Implying that -9+1/2p = 36-1/3p
1/2p+1/3p = 36+9
5/6p = 45
P=54
Reducing the price p by 20%:
0.8*54=43.2

Part 2
Initial Investment = 20m
Annual production = 5m
Net Present Value = PVIFA5yrs,10% - Initial Investment 
= 5,000,000*3.7908 - 20,000,000
18,954,000-20,000,000= (1,046,000) Which is a loss in investment
Conclusion:
Reduce the price by 20%.